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3168 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 39, NO. 11, NOVEMBER 2011

Temporal Development of Ozone Generation inElectron-Induced Corona-Discharge Plasma

T. Vijayan and Jagadish G. Patil

AbstractOzone (O3) generation and its temporal develop-ment to steady state are investigated in a precise model using allhigh-rate reactions for various conditions of gas pressure (P),electron density (ne), and temperature (T) of an evolving elec-tron-induced O2 corona plasma. Densities of O and (O3) radicalsare determined from their gross formation and destruction. Net(O3) density so attained in steady state at T = 300 K is over1025 m3 for P bar and ne 10

15 m3. However, net Odensity for the same is lower 1020 m3 even though O densityexceeded (O3) density in early times of formation. It is shown that(O3) density reduced with temperature heated by discharge incorona, while O density reduced with T up to 500 K and thereafter

increased to

1021

m3

with still higherT

. Both O and (O3)densities varied proportional to the electron density enhanced byavalanche in corona. (O3) varied proportional to pressure, and Oexhibited swing to inverse proportionality with larger P.

Index TermsOxygen discharge, particle balance, radical evo-lution, reaction rates, steady state, temporal buildup.

I. INTRODUCTION

THE subject of evolution and destruction of ozone (O3)is currently a live topic for theoretical as well as ex-

perimental studies particularly on the development of high-

concentration ozone generators [1][4]. In nature, ultraviolet

(UV) rays in sunlight impinge oxygen molecules O2 and pro-

duce O radicals. O radicals, in turn, join with free O2 and

form ozone. These reactions are however reversible. In view

of this and also as processes in nature are very weak, they

yield only small (O3) concentrations less than subparts permillion, whereas the reactions attain enhanced levels when

carried out in a laboratory in controlled conditions and yield

large concentrations useful for numerous applications including

many biochemical processes. This is particularly so by using

electrons [5] as source in place of UV.

In the aforementioned context, most of the two-body and

three-body interactions involving electron, O2, O, and O3 are

well known, and their reaction rates are available in the lit-

erature [1][4]. Of the same, however, only a few reactions,viz., (e, O2), (O,O2, [O2]), (O,O2, [O]), (O,O2, [O3]), (e, O3),(O,O3), (O2,O3), (O3,O3), and (O,O, [O2]), are large enough

Manuscript received April 6, 2011; revised July 4, 2011; accepted August 24,2011. Date of publication October 13, 2011; date of current versionNovember 9, 2011. This work was supported by the Department of Scienceand Technology, Government of India.

The authors are with the Pillais Institute of Information Technology, Engi-neering, Media Studies and Research, Dr. K. M. Vasudevan Pillais Campus,New Panvel 410 206, India.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPS.2011.2166980

to contribute significantly to net particles that evolved from

the reactions. Particles in square brackets in aforementioned

three-body reactions denote the catalyst particles aiding the

reactions. The effect of other reactions, which are not listed

here, are either negligible or all put together make only a minute

correction to the overall results.

In earlier work [5], the evolution of ozone was investigated

in a cold corona discharge formed inside the anodecathode

(AK) annular gap of cylindrical diode of axial symmetry. The

axial cathode of this innovative diode is formed of a large

number of pointed nozzles which are located symmetrically ondifferent radial planes on the same cylindrical cathode mast.

The nozzles here, in addition to injecting oxygen into the

AK gap, created high electric fields over their tips causing

field emissions and paved the way for the formation of corona

plasma discharge. Electrons in this plasma multiplied through

avalanches and formed O radicals by two-body interactions in

background O2. Alongside, formation of O3 occurred in three-

body interactions. Destruction of O3 also happened side by side

through two-body collisions. Thus, the background gas evolved

transiently into a steady-state mixture of O2, O, and O3.

In previous work [5], ozone concentrations were not esti-

mated precisely as there was a confusing picture regarding the

important reactions to be included in modeling where afore-mentioned works [1][4] and others [6][10] employed only a

few of aforementioned high-rate reactions in their models. For

example, [6][8] did not include the all-important two-body

O3 destruction term (e, O3). Also, (O3,O3) destruction term,which is high in the high-O3-density regime, was omitted. The

aforementioned two terms are also important for reinduction

of O radicals into the system. In addition, [6] and [8] did not

include the three-body, namely, (O,O2, [O3]) and (O,O2, [O]),reactions of O3 formation which are peaked with higher O and

O3 present particularly toward the steady state. Similar defi-

ciencies are noted in [9] and [10] even though reaction (e, O3)

was included in their models. In view of these, it was hard toanswer the question at that stage. In the situations, we estimated

ozone concentrations in [5] in more of a qualitative way than

quantitative. We now take up the aforementioned issues and

find appropriate answers in this paper through application of all

the important reactions combined together in a self-consistent

correct model and computation scheme.

Thus, this paper provides near complete simulation model

of oxygen radical evolution by including all-important reaction

terms of formation and destruction. In addition, the present

model is extended to determine the radical species created by

enhanced electron densities in avalanche conditions of corona

and also at the higher temperatures in a discharge-heated

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VIJAYAN AND PATIL: TEMPORAL DEVELOPMENT OF OZONE GENERATION 3169

corona. The computed results are compared with observations

in experiments, and the model is validated.

After introducing the topic in Section I, major reactions

leading to formation of radicals in oxygen corona plasma are

described in Section II along with their rate equations. A

simulation model on these lines, for given boundary conditions,

is also presented in Section II. Results of simulation studiesare described and discussed in Section III. Conclusions are

offered in Section IV. All SI units are used in present theoretical

treatment unless stated otherwise.

II. MODELING OF OZONE FORMATION

A. Major Ozone-Forming Reactions

Ozone (O3) is formed mainly in the following three-bodyinteractions and respective reaction rates [4] k3a, k3b, and k3cin m6/s

O + O2 + [O] O3 + O (1)k3a = 2.15 10

46 exp (345/T) (1a)

O + O2 + [O2] O3 + O2 (2)

k3b = 6.9 1046 (300/T)1.25 (2a)

O + O2 + [O3] 2O3 (3)

k3c = 4.6 1047 exp (1050/T) (3a)

where T is temperature which could be high in a discharge-heated corona and limit the ozone output. O radicals in (1)(3)

are initially made available from eO2 collisions with reaction

rate k1

e + O2 O + O + e (4)

k1 = 2 1015 (m3/s). (4a)

Oxygen dissociation by electron impact here depended on

electron density and energy distribution as described in previ-

ous work [5]. Dependence of latter on discharge current, gas

pressure, device geometry, electric field (E), etc., also has beenexamined with ne and Eshown to be nonuniform.

Destruction of O radicals also takes place alongside O and

(O3) formations. This occurs through (1)(3) as well as throughthe following reaction:

O + O + [O2] 2O2 (5)

k2 = 3.8 1042 exp (170/T)/T (m6/s). (5a)

On the other hand, (O3) reverts to O2 through the two-bodyreactions given hereinafter with rates in m3/s

e + O3 O2 + O + e (6)

k4a = 5 1015 (6a)

O + O3 2O2 (7)

k4b = 1.8

10

17

exp (

2300/T) (7a)O2 + O3 2O2 + O (8)

k4c = 7.3 1016 exp (11400/T) (8a)

O3 + O3 O + O2 + O3 (9)

k4d = 1.65 1015 exp (11400/T). (9a)

Depletion of O also takes place through reaction (7) while

reinduction of O into the system takes place also through(6)(9). Accuracy of the rate equations previously mentioned

is well known and generally accepted [1][10]. However, many

have not included all of them in their models. Our attempt

in present work is to include all the aforementioned reactions

together in a self-consistent simulation model to enable precise

determination of particles evolved in reactions. This was not

done earlier.

B. Simulation Model

The number density rates attained by the particles from

reactions (10)(18) are grouped in the following heads:

(a) O3 formation

nr112 =n1n1n2k3a (10)

nr122 =n1n2n2k3b (11)

nr123 =n1n2n3k3c (12)

(b) O formation

nre2 = nen2k1e (13)

(c) OO reversion

nr112a = n1n1n2k2 (14)

(d) O3 reversion

nre3 =nen3k4a (15)

nr13 =n1n3k4b (16)

nr23 =n2n3k4c (17)

nr33 =n3n3k4d (18)

where ne, n1, n2, and n3 are the electron, O, O2, and O3

densities, respectively. The resulting net O3 formation anddestruction rates are

n3f = nr112 + nr122 + nr123 (19)

n3d = nre3 + nr13 + nr23 + nr33 (20)

which give rise to increase in O3 density in time step t as

n3 = (n3f n3d)t (21)

and density n3(t) at any instant (t) given as

n3(t) = n3(to) + n3 (22)

where to = (t t).

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Similarly, O formation/destruction rates and increase in its

density are

n1f =nre2 + nre3 + nr23 + nr33 (23)

n1d =nr13 + nr112a + nr112 + nr122 + nr123 (24)

n1

= (n1f

n1d)t

(25)

n1(t) =n1(to) + n1. (26)

Then, resulting n2(t) is given from continuity and conserva-tion as

n2(t) = n2(t = 0) 3n3/2 n1/2 (27)

which equals the sum of O2 reversals at steady state from

(14)(18)

n2(t) =n1n1n2k2+nen3k4a+n1n3k4b+n2n3k4c+n3n3k4d.(28)

C. Initial Conditions and Computations

We describe here an infinitely large volume corona plasma

of unbounded limits, uniform densities, and temperature. The

initial densities at time t = 0 are n1 = 0 and n3 = 0, and thepredefined finite values are n2, ne, and Tquantities. Employing(10)(28) transiently and solving them iteratively, n1 and n3 areevaluated to steady state for the condition of

3n3/2 + n1/2 + n2(t) = n2(t = 0). (29)

Time step t = 1 ns is used in the calculations. Results so ob-

tained of O2 corona plasma of various temperatures T, electrondensities ne, and gas pressures P are presented hereinafter anddiscussed.

III. RESULTS AND DISCUSSIONS

The temporal development of O3 formation rates at tem-

perature T = 300 K, oxygen pressure P = 2 bar, and electrondensity ne = 10

15 m3 calculated from (10)(12) is plotted and

compared in Fig. 1. As seen in Fig. 1, the reaction (O,O2, [O2])is maximum at all times. Reactions (O,O2, [O]), althoughhigher than reactions (O,O2, [O3]) in initial times, are lower

than latter in later times. O3

destruction rates [(15)(18)] plot-ted in Fig. 2 in similar conditions show that the reaction (e, O3)

is maximum followed by (O,O3), (O2,O3), and (O3,O3) inthat order. A higher net O3 formation rate deduced from Fig. 1

compared to the net O3 destruction rate derived from Fig. 2

allowed the O3 concentration in reaction space to accumulate

and increase with time. Moreover, finally, the two net rates

equaled with passage of time and established a steady state of

constant O3 concentration as shown in Fig. 3.

Results of O formation reactions show that the rate of (e, O2)

is maximum followed by (e, O3), (O2,O3), and (O3,O3) in thatorder, while O destruction rate given by (O,O2, [O2]) is max-imum followed by (O,O2, [O]) and (O,O2, [O3]). Destruction

by (O,O2, [O3]) overtook that by (O,O2, [O]) as higher O3 wasmade available with time. The net formation and destruction

Fig. 1. Ozone formation rates computed from major reactions (1)(3) andplotted against time in given oxygen corona plasma with pressure (P), tem-

perature (T

), and electron density (ne

).

Fig. 2. Ozone destruction rates computed from major reactions (6)(9) andplotted against time in the same conditions with those in Fig. 1.

rates here show similar trends as those in O3 case and attained

steady states with typical lower values than O3. Here, the net

O formed in early times is higher than that of O3 as shown

in Fig. 3 which helped the creation of more O3

in later times.This along with high life times of O3 caused accumulation of

more O3 and a net exceeding the O net in later times. In the

process, saturation of both the species took place at steady state

as in Fig. 3. In the event, concentration attained by O3 is a few

orders higher than O, and n1 tended to a plateau earlier around107 s due to short O life. These are accompanied by fall of O2density toward steady state as shown in Fig. 3. Particle densities

computed for different O2 pressures (P) are also plotted in thesame figure which shows higher O3 densities of order pressure.

O density at higher pressures although higher in early times

exhibited swing to lower values in later times.

The temporal variation of O and O3 densities at different

temperatures (T) resulting from (1a)(9a) is shown in Fig. 4for P = 2 bar and other conditions same as those in Fig. 3.

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VIJAYAN AND PATIL: TEMPORAL DEVELOPMENT OF OZONE GENERATION 3171

Fig. 3. Temporal buildup of particles O2, O, and O3 densities formed insidethe reaction space at the various pressures (P) in given conditions culminating

to steady state. Reaction rates given in Figs. 1 and 2 were used for getting theO3 plot (2). Rates similarly computed were used in plots (1) and (3) of O3 andall O plots. Observed value of O3 at P = 1 bar is included for comparison.

Fig. 4. O3 and O density variations at different temperatures (T), P = 2 bar,and other conditions same as those in reaction space in Fig. 3.

The temperatures here are representative of those in a corona

heated by the discharge current in typical range of 10100 A

of plasma diode [5]. O3

densities shown in Fig. 4 are lower withhigher temperatures due to the larger O3 dissociations withT. Odensity as seen in Fig. 4 also reduced with higher temperatures

up to 500 K but showed increasing trend with further increase

in T. This is due to the overall net effect of (10)(18) with T.Fig. 5 plots the temporal O and O3 density variations with

electron density ne as a parameter for P = 2 bar and otherthings same as those in Fig. 3. Higher ne here is attainedthrough electron multiplication by avalanche in corona [5].

Fig. 5 shows that both O and O3 densities increased propor-

tional to ne.O3 concentrations observed in [1] in steady-state generation

for 1-bar pressure are around 6 1023 m3 and are shown

along with the present simulation in Fig. 3. Smaller observeddensity compared to the simulation results here is attributed to

Fig. 5. O3 and O density variations at different electron densities (ne), P =2 bar, and other things same as those in corona plasma in Fig. 3.

heating in gas by the discharge current in the diode experiments

as reasoned in [1]. Similar experimental results with heating are

noted in diode in [11]. These comparisons amply validate the

present simulation model.

IV. CONCLUSION

This paper gives a near complete model of O3 evolution in

electron-induced O2 discharge plasma by including all major

reaction terms. Results from the model show that, although

the early O3 density attained was lower than that of O, ozone

density steadily rose to orders of magnitude higher than O

toward steady state as more and more O radicals are madeavailable with time for the O3 genesis. Steady-state O and

O3 densities so formed are 1020 and 1025 m3, respectively,

for pressure P bar, electron density ne 1015 m3, and

temperature T = 300 K. Ozone density however decreasedwith higher T that existed in a discharge-heated corona. Odensity for the same conditions indicated reduction up to 500 K

and then increased with higher T. An avalanche-enhanced nein corona gave higher densities of both O and O3 while higher

pressures gave higher O3, but O densities swung from higher

side at early times to lower side at the later times to steady state.

Simulation results are compared with observed values.

ACKNOWLEDGMENT

The authors would like to thank Dr. K. M. V. Pillai and

Dr. D. Pillai for the encouragements and Dr. A. K. Das for the

discussions.

REFERENCES

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[2] J. Kitayama and M. Kuzumoto, Theoretical and experimental study on

ozone generation characteristics of an oxygen-fed ozone generator insilent discharge, J. Phys. D, Appl. Phys., vol. 30, no. 17, pp. 24532461,Sep. 1997.

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[3] B. Eliasson, M. Hirth, and U. Kogelschatz, O3 synthesis from O2 indielectric barrier discharges, J. Phys. D, Appl. Phys., vol. 20, no. 11,pp. 14211437, Nov. 1987.

[4] R. Peyrous, P. Pignolet, and B. Held, Kinetic simulation of gaseousspecies created by an electrical discharge in dry or humid oxygen,

J. Phys. D, Appl. Phys., vol. 22, no. 11, pp. 16581667, Nov. 1989.[5] J. G. Patil and T. Vijayan, Characteristics of high-tension induced

corona-discharge plasma in ozone generator diode, IEEE Trans. Plasma

Sci., vol. 38, no. 9, pp. 24222427, Sep. 2010.[6] K. Yanallah, S. Hadj Ziane, A. Belasri, and Y. Meslem, Numericalmodeling of ozone production in direct current corona discharge, J. Mol.Struct.THEOCHEM, vol. 777, no. 13, pp. 125129, Nov. 2006.

[7] P. Pignolet, S. Hadj-Ziane, B. Held, R. Peyrous, J. M. Benas, and C. Coste,Ozone generation by point to plane corona discharge, J. Phys. D, Appl.Phys., vol. 23, no. 8, p. 1069, Aug. 1990.

[8] C. Gutierrez-Tapia, E. Camps, and O. Olea-Cardoso, Pertubative methodfor ozone synthesis from oxygen in a single discharge, IEEE Trans.Plasma Sci., vol. 22, no. 5, pp. 979985, Oct. 1994.

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[10] J. F. Loiseau, F. Lacassie, C. Monge, R. Peyrous, B. Held, and C. Coste,Numerical simulation of ozone axial and radial distribution in a cylindri-cal oxygen-fed ozonizer, J. Phys. D, Appl. Phys., vol. 27, no. 1, pp. 63

73, Jan. 1994.[11] T. Vijayan and J. G. Patil, High concentration ozone generation in lab-

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T. Vijayan received the Ph.D. degree in physics fromthe University of Mumbai, Mumbai, India, in 1983.

He started his carrier as a Teacher in physics withthe Government College Kasaragod, Kasaragod,India. He is currently a Professor in physicswith the Pillais Institute of Information Technol-ogy, Engineering, Media Studies and Research,Dr. K. M. Vasudevan Pillais Campus, New Panvel,

India. Prior to that, he was a Senior Scientist withBhabha Atomic Research Centre, Mumbai, andwas engaged in research on generation and transport

of particle beams and plasmas and their applications and interactions withvarious targets.

Jagadish G. Patil received the M.Sc. degree inphysics from the University of Mumbai, Mumbai,India, in 2002.

He is currently a Senior Research Fellow inphysics with the Pillais Institute of InformationTechnology, Engineering, Media Studies and Re-search, Dr. K. M. Vasudevan Pillais Campus, New

Panvel, India. Prior to that, he was a Project As-sistant with the Indian Institute of Geomagnetism,Mumbai, and was engaged in observatory dataanalysis.

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