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Ozone synthesis from oxygen in dielectric barrier discharges
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1987 J. Phys. D: Appl. Phys. 20 1421
(http://iopscience.iop.org/0022-3727/20/11/010)
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J. Phys. D: Appl. Phys. 20 (1987) 1421-1437. Printed in the UK
B Eliasson, M Hirth and U Kogelschatz
Brown Boveri Research Center, CH-5405 Baden, Switzerland
Received 3 November 1986
Abstract. A comprehensive model of ozone generation in dielectric barrier
discharges is presented. The model combines the physical processes in the
micro-discharges with the chemistry of ozone formation. It is based on an
extensive reaction scheme including the major electronic and ionic processes. The
importance of excited atomic and molecular states is demonstrated. Theoretical
limits are given for the ozone production efficiency and the attainable ozone
concentration. The most important parameters influencing the performance of
ozonisers are identified. All theoretical predictions are compared to measured data.
of ozone production aswell as thesignificance of ozone
destruction by electronic collisions.
1. Introduction
Ozone, historicallymainlyused for the treatment of
drinking water, is known to be a potentbactericide and
viricide. It is one of the strongestoxidising and bleaching
agents and it has the important property that it decays
without residues that could be harmful to the environment, Since the on-site production of ozone requires
only air and electricity no transport of potentially dangerouschemicals
is involved in ozoneapplications.
These are the main reasons why ozone is increasingly
usedforbleachingandoxidisingpurposesas
well as
being considered for the elimination of NO, from flue
gases of power plants. Larger ozone installations have
reached the megawatt level producing some hundred
kilograms of ozone per hour. Even larger plants producing tons of ozone per hour are in the design stage
making ozone production one of the most important
examples of plasma synthesis.
In this paper we describe a theoretical treatmentof
ozone formation in dielectric barrier discharges which
starts from basic physical principles and can predict the
majorexperimentaltrends of ozoneformation.Our
model has some inherent advantages over models proposed in the past. Homogeneous models of ozone formation in gas discharges were presented by Devins [l]
and, more recently, by Yagi and Tanaka [2]. Attempts
to treat the structure of the discharge were published
by Sugimitsu andco-workers [3] proposingasimple
avalanche model and by Gibalovandco-workers [4]
who presentedaveryextensivenumericalmodel.
Goldman and Lecuiller [5], who have investigated corona discharges, suggested that ozone formation cannot
beexplained onthe basis of ground-statereactions
alone.Ourcalculationsdemonstratethe
influence of
excited atomic and molecular states on the
efficiency
+ 17 $02.50 @ 1987 IOP Publishing
0022-372718711 11421
Ltd
2. Characterisation of micro-discharges in a dielectric barrier discharge
Ozone is almost exclusively produced in dielectric barrier discharges (silent discharge), a configuration
first
proposed by Siemens in 1857 [6]. Its main characteristic
is the presence of a dielectric layer between the
discharge gap and at least one of the electrodes. While
traditional ozonisers use alternating voltages
of 50 or
60 Hz,modernhigh-power
ozonisers arefedfrom
thyristor controlled frequency converters operating at
a typical frequency range from 0.5-5 kHz.
The presence of the dielectric leads to the formation
of a large number of micro-discharges of nanosecond
duration. These micro-discharges are statistically distributed with respect to space and time. The intermittent
nature of the discharge was recognised as early as 1932
by Buss [7] and in 1937 by Klemenc and co-workers[g].
The nature of these micro-discharges was investigated
by visualisation of the charge patterns on the dielectric
[7,9-121, by analysing
throughLichtenbergfigures
‘hairs’ on current oscillograms [13-151 and by obtaining
image intensifer recordings [13, 141.
These investigations clearly show that in dielectric
barrier discharges in oxygen or air at about atmospheric
pressure the charge transport across the gap is brought
about by a large number
of short-lived micro-discharges.
Each micro-dischargeconsists of athinalmost
cylindrical channel with a constricted electrode spot at the
metal electrode and spreads into surface
a
discharge on
the dielectric. The charge patterns ondielectric
the
form
1421
B Eliasson et a/
Figure 2. Transferred charge of a micro-discharge (each
point represents an average of 100 measurements of both
polarities, dielectric barrier:2 mm glass, E = 5;
pressure = 2 bar).
Figure 1. Plate ozoniser studies of micro-discharge
properties. (a) Photographic Lichtenberg figure (taken in
air) original size: 38 mm x 70 mm; (b) electrode
configuration (not drawn to scale) with current probe; (c)
measured current pulse in oxygen.
stars or diffuse circles depending on polarity. Theycan
be recorded as
a photographic Lichtenbergfigure (figure
l(a)) if a photographic plate is used as a dielectric in a
small plate ozoniser (figure l(6)). The incorporation of
a well shielded fast current probe (Tektronix
(3-1) into
the ground electrode
allowed usto obtain currentpulses
of individualmicro-discharges
in anozoniserconfiguration. The aimwas to isolateasegment
of the
electrode small enough to behit by one micro-discharge
at a time,asproposed originally by Hirth [15]. We
reduced the areaof the segmentuntil in the final version
we used a cylindrical pin of 1 mm diameter [16]. Care
was takenthatthefrontsurface
was flush with the
electrode. A gap of 0.1 mm between the measuring pin
and the electrode was filled with epoxy. Running this
plate ozoniser with 400 Hz we detected a micro-discharge hitting the measuring pin roughly every 5 ms.
Figure l(c) shows such a micro-dischargecurrent pulse.
The peak currentwas typically 0.1-0.5 A, its half width
t,about 2 ns, considerably shorter thanwas previously
assumed [9, 111. The leading edge is presumably not
resolved by our measuring circuit which had a risetime
of 1 ns.
1422
To determinethechargetransported
in a microdischarge we replacedthecurrentprobe
by a small
condenser (1 nF). The measured voltage jump of the
condenser showed appreciable scatter (up to
a factor of
five). The data presented in figure 2 were obtained by
averaging over 100 micro-discharges of both polarities.
The measured charge increases nearly linearlywith gap
spacing [ 161 and agrees with values presented in [13].
Theoretical considerations on streamer breakdownlead
to the same order of magnitude. They also predict no
variation of the charge with pressure [17].
3. Initiation and extinction of a micro-discharge
Initial electrons cangrow intoavalanches whenthe
electronproduction(ionisation,detachment,
release
from cathode) surpasses the
losses (mainly attachment).
When the propagating electron cloud reaches a critical
density locally a micro-discharge is formed. For slowly
varying electric fields E ( [ ) this breakdown condition is
given by the Paschen curve which is mainly a function
of the product particle density n times gap spacing d.
Three aspects are important with respect to ozonisers.
(i) The small gap spacings of typically 1-3 mm
require noticeablyhigher field strengths for ignition
than wider gaps at the same particle density [M].
(ii) Considerable timelags (up to 1 ms)are observed
in such electrode configurations [19]. During the time
lag the alternating appliedfield can reach values noticeably higher than the stationary breakdown field. Typical effective reduced field strengths are in the range
100Td S E/n S 200 Td (1 Td= 10"' V cm2).
(iii) The time delay and thus the effective
field is
influenced by the second Townsend coefficient y which
Ozone synthesis from oxygen
describes the number of secondary electrons released
from the cathode, This coefficient can vary by severai
orders of magnitude.It is afunction of thesurface
properties of the metal electrode and the dielectric, in
addition to the gas properties, and strongly influences
the initiation of a micro-discharge. For small nd, high
y and slowly varying fields a micro-discharge
will be
started by a succession of Townsend avalanches. For
large nd, low y and/or fast varying fields (pulsed ozonisers) a micro-discharge is initiated by a streamer, that
produces enough charge-induced field distortion at its
headtoachievebreakdown
inasingle
transit.Both
cases can occur in ozonisers depending on conditions
POI.
As soon as current flow is initiated in a micro-discharge,charge will starttoaccumulate
in thearea
wherethemicro-dischargehitsthedielectric.
As a
consequencethe field in thegap is reduced.When
the field is reduced to such an extent that attachment
becomes more important than ionisation and detachmentthedischarge
is choked.Fromourcurrent
measurements we know that this process is terminated
withinafew
nanoseconds.Thearresteddischarge
column behaves in many respects like a transient glow
discharge
[21,22].
From
side-on
image-intensifier
records [13, 141 we know that the radius
of amicrodischarge channel is of the order of R = 100 p . With
these data we can determine the order
of magnitude
of the most important propertiesof the micro-discharge
channel: ( n = 2.4 X 1019cm-3, d = 0.1 cm)
Total charge
current density
electron density
energy density
reduced field
electron energy
Q - 10"O AS
j - lo3 A cm-?
n, - 10l4cm-3
J1 J cmp3
E/n 100-200 Td
about 5 eV.
e
+ O 2+ 2 0 + e
(R7)f
(1)
and a subsequent three-body reaction
0+0
2
+ M+
0,+ M
(R9)
(2)
where M = 0. O2 or O 3 is a third collision partner.
Since reaction R7 is extremely fast the timescale for 0
formation is essentially givenby the width of the current
pulse t l= 2 ns. It can be shown [24] that in our model
the duration of the current pulse is mainly determined
by the rear slope of the E / n pulse causing the current
(see figure 4 later).
Ionisation and attachment being the main processes
where p1 andaretherate
coefficients forionisation
and attachment which depend strongly on E/n. On the
right side of equation (4) thefirst term characterises the
gas and the second the
field pulse. From our current
measurements we know that t l = 2 ns.
According to equation (2) the formation of O3 can
be characterised by the time constant
at 1 bar and 300 K.
The O 3 concentrationhas initially thesamegeo0 concentration namely
metricaldistributionasthe
the micro-discharge volumeof approximately R = 100 p
radius. It thendiffuses into the background volumewith
a diffusion time constant
-
73 = n R 2 / D =
Due to the minute energy deposition the heavy particle
temperature will remain close toroomtemperature.
The micro-discharge is interrupted long before leader
formation or spark transition can occur. Since the gas
in the discharge column is not heated up current flow
stops at a finite field strength slightly below the breakdown field [15, 231. The nextmicro-dischargeatthe
same position can occur only after the
field has been
raised again to fulfil the initiation condition. In the mean
time, micro-dischargeswill strike at other positions. The
dielectric,thus,hasa
twofold function.It limits the
charge of an individual micro-discharge and, at Same
the
time, ensures that the whole electrode surfaceis evenly
filled with micro-discharges, Ozone is produced only in
themicro-discharges.Therefore,a
realistic modelof
ozone formation in ozonisers has to take into account
the transient conditions in these filaments.
4. Temporal and spatial aspects of ozone formation
Ozone formation is atwo-stepprocessthatStarts
the dissociation of O 2 molecules by the electrons in a
micro-discharge
with
1.6 ms
(6)
where D 0.2 cm' sC1 is the diffusion coefficient of O3
in 02.
We see that the following relation is valid
71
e Z? e t 3 .
(7)
The formation time of oxygen atoms in amicro-discharge is muchsmallerthanthat
of ozoneand,on
the other hand, ozone formation
is much faster than
diffusion
processes
that
dilute
the
concentrations.
Figure 3 schematicdlly shows the channel left behindby
the micro-discharge at different times.
At atmospheric pressure the mean free of
path
atoms
and molecules is of the order of 100 nm, three orders
of magnitudesmallerthanthediameter
of amicrodischarge. This allows us to treat the micro-discharge
volume as a homogeneous continuum. We neglect the
electrode fall regions which have an extension
of less
than 10 pm at 1bar. This is negligible compared to the
length of a micro-discharge given by the gap spacing d.
t The R numbers refer to the reactions listed in the Appendix. All
reactioncoefficients
p, arenumberedaccordingly,
1423
B Eliasson et a/
t=o
l
l
t=T1
standsforavibrationallyexcited
O3 molecule. Our
reaction scheme considers 70 reactions which are listed
in the Appendix. An evaluation of cross sections and
rate coefficients used is contained in [25]1. Very little is
known about the effect of radiation in ozonisers. For
this reason no radiative processes are
included in our
reaction scheme. Our approach
is based on the firm
belief that such modelling schemes should be based
only
on known cross sectionsor ratecoefficients. No attempts
weremadetoadjustparametersorpostulate
new
processes.
6. Numeric modelling of the electric pulse
Numerous attempts have been made to calculate the
electron avalanche breakdown in a discharge gap. The
treatment is complicated by the existence of high local
electric fields due to theaccumulation of space charge at
the avalanche head. Thedeficiency of data on processes
occurring in the neighbourhood of the avalanche head
like photo-ionisation renders the treatment even more
difficult. We refer to the review articles of Lozanskii
[26] and Kunhardt [27]. After the first streamers reach
the electrodes aweakly ionised channelof fairly homogeneous charge density and field strength bridges the
gap. The properties of this conducting micro-discharge
channel are, in many respects, similar to those of the
positive column of a glow discharge.
Our aim is to simulate the temporal behaviour of
this transient glow phase inaccordancewithmeasFigure 3. A schematic diagram of the spatial distribution of
urements and investigate itseffect on ozone formation.
electrons, oxygen atoms and O3 molecules at different
In our numerical model we generate a current pulse
times.
thatcorrespondstoourmeasurements
of individual
micro-discharges by applying an electric field variation
(figure 4 ( a ) ) with linear risetime (ll) and exponential
We assume a rectangular radial particle densityprofile.
Trial calculations with Gaussian
profiles had only a small decay (time constant t 2 ) . Since the rate coefficients for
electronicprocessesdepend strongly on the electron
effect on theresults.
energy we calculate the rate coefficients as a function
We calculate the evolution and
decay of different
of the reduced electric field E / n by solving the Boltzparticle species of a homogeneous volume subjected to
mann equation for electrons in an O2 gas. We use a
a short field pulse. The field pulse is chosen in such a
code which was based on the work of A V Phelps and
way as to produce a current pulse in agreement with
his associates and which was documented by Luft [28].
the measured pulses. Since all reactions are terminated
A Monte Carlo simulation of electrons inoxygenat
within 10 p s we do not consider diffusion processes. In
1bar and 150 Td based on the model
given in [29]
a typical ozoniser discharge a volumeelement travelling
through the discharge gap
will be subjected to the action shows that the timescale for electrons to reach equilibrium is less than lo-" S . This is much shorter than
of several hundred micro-discharges. We assume that
our
field variation. So it is justified to use equilibrium
the local ozone concentration created by a micro-diselectron
energy distributions.
charge hasdiffused into the background before thenext
4 shows the appliedfield pulse, the calculated
Figure
micro-discharge occurs in the same volume element.
currentdensityandtheevolutionand
decay of the
differentchargedparticles.Forthistypicalpulsethe
calculations show that the maximum current density of
5. Reaction scheme
about 550 A cm-2 is reached at E / n = 151 Td, a value
that lies considerably higher than the critical
field where
In order to calculate ozone formation
in a micro-disionisation equals attachment(108 Td in oxygen). Above
charge we consider reactions involving electrons, the
the critical field ionisation dominates, below this value
positive ions O + , O i , the negative ions 0 - ,0 ; , O ; ,
attachment is moreimportant. Since attachment in
thegroundstatesO(3P),
0 2 ( X 3 E , ) , O3(lA1) and
O('D), 02(a'A,),OZ(b'
X:),
the
excited
states
t Available on request from the authors.
O z ( A 3E:), 0 2 ( B 3Z;), 02(v) and O ; , where 0:
1424
Ozone synthesis from oxygen
10-6
500
10”
10-8
-
t2
N
Q
Is)
Figure 5. Relative energy losses due to ions as a function
of the electric field decay time constant t2 and the energy
density J, for oxygen.
300
7
100
0
4
8
12
16
6
Electrons
I
~
~
4
2
0
4
16
8
12
Time Ins)
Figure 4. Electrical properties of a micro-discharge.
(a)Assumed variation of the reduced field; (b) electron and
ion currents; (c) relative densities of charged particles.
high that ion recombination is considerably faster than
the drift time, most of the energy will be imparted to
the electrons.
To demonstrate this effect we varied the length of
the current pulse by changing the time constant t , for
the decay of the reduced field pulse. Figure 5 shows the
fraction of energy dissipated by ions. It will become
appreciable only if the pulses are long or the energy
density in the pulse is very low. In the example chosen
in figure 4 about 99% of the pulse energy is fed into the
electrons. In the next section we will investigate what
fraction of this energy can be
utilised for thedissociation
of 0 2 .
7. The dissociation process
pure oxygen is veryfast the electron current will be
terminated before E / n can fall much below this value.
We define the ‘effective field’ as the field at current
maximum (dj/dt = 0). For our current pulses we can
safely state that the effective reduced
field will be in
therange of 100-200Tddependingontheassumed
E/n pulse (maximum, t l , t2). Figure 4(b) shows that the
ion current amounts to
less than 1%of the total current.
The relative particle concentrations plotted
in figure4(c)
indicate a weakly ionised plasma (degree of ionisation
with 0 ; as the major positive ion and electrons
and 0- as the most important negative particles.
Knowingthedifferentchargedparticledensities,
their drift velocities and the field variation we are in a
position to calculate the amountof energy dissipated by
theelectronsanddifferent
ionicspecies.Ithasbeen
claimed [2,9] that half of theenergydissipated in a
dielectricbarrierdischarge is taken up by ions.This
would beanundesirable
loss since ozoneformation
depends mainly on electronicprocesses.Fortunately,
our calculations show that this assumption is not genif they are
erally true. Ions can only take up energy
allowed to drift in the presence of an electric field. If
the field pulse is much shorter than the ion drift time
(about 2 ,us for a 1 mm gap) or, if the ion density is so
The energy-level diagram of O 2 (figure 6) shows that
theFranck-Condonregionforelectronicexcitation
from the ground state favours processes at about6 and
8 eV. They can be related to electron scattering cross
sections with threshold energiesof 6 and 8.4 eV. These
processesaregenerallyassociated
with the Herzberg
\
1
2
3
Internuclear dlstance (AI
Figure 6. Simplified potential energy diagram of 02.
The
arrow indicates the Franck-Condon region for excitation
from the ground state.
1425
B Eliasson et a/
100%
l
1
I
I
l
0
~
0
1
:
5
0
,
f i n (Td)
Figure 7. Distribution of electron energy losses as a
function of the reduced electric field; energy branching in
oxygen.
(A 'X:) and Schumann-Runge (B 32:;) system of the
O 2 molecule
+e
+ 0 ('P) + 0 (3P)
(R7a)
(8)
O
0
0
200
100
Eln ( T d i
Figure 8. Efficiency of atomic oxygen and ozone formation
as a function of the reduced electric field. The parameter
xlo= [O]/[O,]
is the relative atom concentration in a
micro-discharge column.
The numberof oxygen atoms producedby one electron
per cm of path is
n1 = 2p7nv;'
e
+ 0 2 + e + O2 (B 3X:)
+ e + 0 (3P) + o ('D). (R7b)
(9)
Figure 6 also shows that the first reaction includes
contributions from the A' 'A, and cl X; terms. In pure
by
oxygen the excited 0 ('D) atomsarequenched
collision within about 10 ns (see figure 10, later). If O3
molecules are already present a very fast destruction
reaction comes into play
0 ('D)
+ O3+ 2 0 2 .
(R35)
(10)
In order to calculate the rate
coefficient for dissociation
and the energy branchingof the different processes we
used a set of electron impact cross sections [25]which
are to a large extent based on cross sections proposed
by Phelps [30].Figure 7 shows that the combined action
of the twoprocesses (R7a) and (R7b)allows us to utilise
about 80% of the electron energy for the dissociation
processover
afairlywiderange
of reduced field
(100 Td S E / n S 300 Td). At lower fields elastic collisions and rotational and vibrational excitation become
important, at higherfields ionisation predominates.This
isin fair agreement with results obtained in [31] and
[32].It should be pointed out that
this situationis almost
unique in oxygen. In air, for example, we lose a much
larger fractionof the energy due to vibrational
excitation
of N2 molecules.
With these calculations we are in a position to determine how much energy is required for the formation of
one oxygen atom. We again consider the limiting case
that no energyis lost to theions in the pulse. Theenergy
gained by an electron in the electricfield per cm of path
is given by
(12)
where p7 = p? + p? is the dissociation rate coefficient,
n the particle density of O2 and u d the drift velocity of
electrons.
The energy required to obtain one oxygen atom is
given by the ratio of equation (12) and equation (11)
nl
-2-
"
AE
P7
evdE/n'
(13)
This relation is presented in figure 8 as the uppermost
curve together with the result of the complete reaction
scheme without ionic processes. This curve also shows
the maximum obtainable
efficiency for ozone formation,
O3
provided
that
every
oxygen atom
forms
one
molecule. In this casewe obtain approximately 0.22 O3
molecules pereV which correspondstoaminimum
energy of 4.55 eV per O3 molecule.
Reduced fleld , € i n ( T d
Figure 9. Calculated dissociation rate coefficient,p,, as a
function of the reduced electric field.
1426
Ozone synthesis from oxygen
physics of the upper atmosphere.Most of these excited
0 ; molecules(mainlyasymmetricstretchmode)
will
bequenched by collisions with oxygen atoms or O2
and O3 molecules(R66a,R70), but some will react
according to R66b. The reaction rate
of this excitedstate
is about 1600 times larger than that
of the corresponding
ground-state molecule in reaction R11. The influence
of the different reactions can be seen from figure 10.
The charged particles disappear relatively fast leading
to a current pulse of a few nanoseconds duration. The
current density and charged particle concentrations of
this pulse were shown in figure 4 with a linear scale.
Dissociation is very fast and is completed at the end of
O('D) is
the current pulse. The excited atomic state
quenched within nanoseconds. Ozone formation, on the
otherhand, is finishedonlyafter
about lops. The
presence of 0 ; reducesthe final ozone level and
increases the time constant
of ozone formation [39].
While ozone formation accordingto reaction R9 would
have a time constant of 3 ps, this calculation yields a
of 6 p s . This is much closer tothe
timeconstant
measured values of 8-10 ps [39]. Figure 11 shows the
strong influence of the relative atom concentration xl0
on the conversion [O],/[O] as well as the strong influence of vibrationally excited O3 molecules. In the left
part every 0 atom forms an O3 molecule because the
concentration is so low that an oxygen atom, during its
lifetime of about 10 p , only collides with 0, molecules
thus avoiding reactions R11, R12, R66.
In this limitingcase the energy expenditure for ozone
formation(figure 8) will benearly identical tothat
foratomformation.Figure
8 alsoshows thatozone
formation by only considering direct electron impact
dissociation R7 yields the maximum efficiency. The
inclusion of excited O2 molecules and excited O3molecules leads to a decrease of efficiency. The question
arises what influence the ion molecule reactions R18.
The calculated curves of figure 8 show that the ideal
situation, that every 0 atom according to reaction R9
reacts to form oneO3molecule, is obtained only if the
relative atom concentration xl0= [0]/[02]
is less than
efficiency is already
At 1%atom concentration the
halved. This means that only
every second oxygen atom
reacts with an O2 molecule to form ozone. The level
part in figure 8 results from the fact that the dissociation
rate coefficient p 7 has approximately the same slope as
the product udE/n. p7 itself depends strongly on E/n
according to our calculations (figure 9). A comparison
with other publishedvalues and a more completediscussion of the dissociation process in oxygen is given in [33]
and [34].
8. Ozone formation in a single micro-discharge
Wehaveshownthatcomplete
conversion of oxygen
atoms to ozone via reaction R9 can only be achieved
atvery low atomconcentrations.The
relative atom
concentration xl0 is avery importantparameter.It
determines how many oxygen atoms really form ozone
molecules. Reactions responsible for incomplete conversion are, for example
0
+ 0 + M-*
0 2
0+03-
202
+ M(R12)
(14)
(R11)
(15)
+ 0 ; + 202 (R66b).
(16)
and, more important
0
It has been conclusively demonstrated that most of the
O3 molecules formed by reaction R9 are initially in a
vibrationallyexcited
state [35-371. Thisfact is also
stressed by Rawlins [38] in a recent publication on the
Tlme
(SI
Figure 10. The evolution of different particle species after a micro-discharge
(corresponding to the current pulse of figure 4).
1427
B Eliasson
et a/
"_
- 0.20
removed by the coolingcircuit. Theimportance of
efficient heatremoval is demonstrated by figure 12.
Allcurvesshowa
drop of efficiency at raised temperatures the extent of which depends on the relative
atom concentration .xlo. We will show that the relative
atom concentration in a typical microdischargeis of the
order of .xlo
severalorders of magnitudehigher
than was assumedinpreviousmodels
of ozoneformation [2, 41.
l
h
2 0 15
2
\
+
-g
0.10
I
\
-
\ '\,
m
0
\
,
0 05
IO+
x.o
10-2
9. Energy density and atom concentration in a
micro-discharge channel
Relatlve atom concentratlon IO1 / IO2]
Figure 11, The influence of oxygen atom concentration
and vibrationally excited O3molecules on the efficiency of
ozone formation. Broken curve, without 0 ; ; full curve, with
0;.
The energy density immediately after termination
of the
current pulse is given by
R26, R30, R44, R4.5, R48, R60 and R61 have. Also the
influence of otherreactionsproducing oxygen atoms
like dissociative attachment (R2) and detachment (R3,
R4, R6) is of interest. For the pulse shown in figure 10
we calculated the efficiency of ozone formationwith the
complete reaction scheme, including all electronic and
ionic processes, to be 26.3%. Omission of ionic processes for the same conditions( ( E / ~ Z=) ,151
~ Td, x l 0 =
1.8 x
yields an efficiency of 26.6%. This
demonstratesthatunder
typicaloptimisedozoniserconditions ozone is almost exclusively formed from oxygen
atoms that have been provided by electron impact dissociation. The inclusion of excited species or that of
ionic processes lowers the efficiency.
The most
important
parameter
affecting the
efficiency is the atom concentration. For larger atom
concentrations the efficiency drops drastically. On the
right-hand side of figure 8 we indicate anefficiency scale
which is based on the enthalpy of formation of ozone
1.48 eV/molecule or 143 kJ mol-' taken as
100%. In
the reduced field range of 100-200 Td we see very little
dependence on the electric field. The calculations show
that we can expect a maximum efficiency of 33% which
ti of theenergydissipated in an
meansthatatleast
ozoniser will showupasheatand
will havetobe
1
0.25
1
1
8
1
J1 =
I
l
I
I
.
E ( t ) j ( t ) dt.
(17)
In a micro-dischargethe current density
j ( t ) varies much
faster than thefield E(t). If we approximate thespatially
homogeneous electron density ne([)by a delta function
of time we can perform the integrationin equation (17).
where
and F, are the transported charge and thecross section
of the micro-discharge channel.
The relative oxygen atom concentration xlo = [ O ] /
[O,] is linked to the energy density J1in the following
way: fromreactions 7 a and 7 b we getthe following
expression for the atom concentration per pulse (p, =
P? + P ; ) :
[O] = ~ 1 0 [ 0 2 1 = 2
~ 7 [ 0 2 ne(t>
1
(19)
By again assuming that the electron density
varies much
faster than other parameters involved we get
'
l
Iox
.xlo
= 2p7
QC eFcud
2P7
eud(E/n)eff
J1
n'
(20)
The ratio of 2p,/(eudE/n) is almost constant according
to figure 8.
Thus the strength
of a micro-discharge can be characterised either by the energy density immediately after
0
termination
the pulse,currentof the
J l , or by the
relative atom concentration .xlo reached at that time.
The two parameters are linked by equation (20). Since
xIuis the parameter that governs ozone formation we
100
300
500
700
900
1100
prefer the use of xlo.It is the most important parameter
Temperature ( K 1
characterising a specific ozoniser. Its value can beinfluenced by gap spacing and pressure, choice of electrode
Figure 12. The influence of the gas temperature on the
and dielectric as well as by the feeding circuit.
efficiency of the ozone formation.
m
1428
Ozone synthesis from oxygen
From 3 3 we know that the order of magnitude of
the energy densityof a micro-discharge ( p = 1bar, d =
1mm) is lop2J cm-3 or 2.5 X
eVperparticle.
According to equation (20) the order of magnitude of
xl0 will be 10-4-10-3. These estimates were based on
the measured charge and channel diameters extracted
from
side-on
image-intensifier
records,
which,
especially in oxygen,are very faint.Clearly,amore
precise determination of xl0 is desired. Since the determination of the parameterxl0is essential for modelling
the performance of ozonisers and since we claim that it
is orders of magnitude larger thanwas assumed in other
models we want to discuss its determination in more
detail.
The onlydirectmeasurements
of atomconcentrations in a dielectric barrier discharge were reported
by Viol and co-workers [40]. He determined atom concentrations in a pulsed low-pressure discharge ( p = 311mbar) by resonance fluorescence of O(%O) atoms.
Viol concludedthattherelativeconcentration
of
ground-state O(3P)atoms was about
Sinceaccording to [l41 the diameter of the micro-discharge column
contracts with rising pressure we expect xl0to be larger
at atmospheric pressure.
Wefoundtwomethodsthat
furnishinformation
about the atom concentration in a micro-discharge, If
we measure the efficiency of an ozoniser at very low
([O,] < 0.5%) we
backgroundozoneconcentration
essentially determine the efficiency of a single microdischarge. It turns out that
this efficiency has a small
butdetectabletemperaturedependence:
it dropped
by
about 3.3% over 50". We varied the temperature
changing the temperature of the cooling circuit. At the
nd constant
same timewe adjusted the pressure to keep
in thedischargegap in order to keep the
discharge
conditions as constant as possible. A comparison with
xl0
figure 12 shows that this variation corresponds to an
value of the order of
In a second experiment we added traces of NO2 to
the feeding gas and found thatthey had a drastic effect
on the efficiency of ozone formation. About 1%0NOz
will completely inhibit 0, formation. An evaluation of
this effect with an extended reaction scheme including
the NO, reactions showed that NO2 can be used as a
probe to determine.xlo. We find that xl0 = 1.8 X loe3for
1 mm gap at 1 bar and that .xlo increases with pressure.
Figure 13 shows the NO2measurements and the derived
atom concentrations in the micro-discharge for a 1 mm
gap at different pressures.
10. The influence of the gas temperature
10.1. Temperature in the micro-discharge channel
Some of the rate coefficientscharacterisingchemical
reactions in the micro-discharge
channel
depend
strongly on the gas temperature. Thus it is essential to
know the temperature in the micro-discharge channel
at the time the chemical reactions occur:
z1 < t < t2.
10
0
(bl
1
2
3
4
p (bar)
Figure 13. (a) Measured NOp addition necessary to
suppress ozone formation completely in a micro-discharge.
(b) xlois the derived relative oxygen atom concentration.
Let us again consider the situation where we have no
energy losses to ions. Initiallywe feed 80% of the energy
into the dissociation process (A 3E: and B 3E; states)
and about 20% of the energy into other excited states.
Part of this energy will eventually show up as kinetic
energy of the heavy particles after recombination and
de-excitation to the ground states. The questionis how
fast these thermalisation processes will occur in comparison with the few microseconds it takes for ozone
formation.We canestimateanupper
limit forthe
temperature rise in the reaction channel [24]
If 33% of the energy is spent on ozone formation, at
most 67% is available for temperature increase. With
J12: 2 X lo-* J cm-3, p = 1.3 X
gcm-3 and cp =
0.92 J g" K" we estimate
AT,
11 K
AT, is proportional toJ , or tox l 0 and will increase with
gap spacing and pressure. This increase of about 10 K
(1 mm, 1 bar) can be reached only after all atoms have
disappearedand all O2 and O3 molecules are in the
ground state. Perhaps, half of thisvalue would be a
reasonableassumptionformodellingpurposes.This
local temperature increase is much smallerthan was
1429
B Eliasson et a/
previouslyassumedin
[41] and is spread by thermal
conductivity with a time constant comparable to thatof
the diffusionprocess for oxygen atoms (z2). Thus, in
principle we shall not make a large mistakeby assuming
that the temperature for the chemical reactionsis close
to the average temperature in the gap, i.e. we assume
ATc = 0. The average temperature is determined by
power input and heat removal in a specific geometry.
10.2. The average temperature in the discharge gap
Since many of the rate coefficients used in our reaction
scheme depend on temperature we have to know the
average gas temperature in the discharge gap, Itcan be
derived from thefollowing consideration. In the narrow
gapstypical for ozonisers, after a
few centimetres of
entrancelength, we reachastationarytemperature
ATgwill
distribution. The average temperature increase
be determined by the balance between the power dissipated in the gap (minus the amount used for ozone
formation) and the heat removal
by radial heat conduction to the cooled electrode(s). Thus
ATg = a(d/A)(P/F)(1 - r )
(22)
where A is the heat conductivity of the gas, and P / F is
the power divided by the electrode area. If we assume
that the poweris evenly dissipated in the volume of the
discharge gap we obtain a parabolic radial temperature
profile [15,42] and the averagingcoefficient a takes the
value
for coolingof one surface
for cooling of both surfaces.
We also neglect the small
micro-discharge.
+ AT,.
Let us first start with a model calculation disregarding
the diffusion process after each pulse. In this simplified
calculation we starteachpulseattheozoneconcentration reached at the endof the preceding pulse. In
figure 14 we see that at low concentrations there is a
linear build-up (range I). At higher concentrations the
rate decreases (range 11) and the concentration finally
saturates (range 111). The saturation concentration ,x3,
depends strongly on the assumed average temperature
in the gap. Once the saturation concentration
is reached
each additional micro-discharge destroys much
as ozone
as it creates, thus resulting in a net zero production or
zero efficiency. The strong temperature dependence is
mainly due to reaction R11
0
+0
(23)
3
(R11)
-+ 202
(24)
the reaction coefficient of which is
pI1= 1.8 x lo-" exp(-2300 T - ' ) cm3 S - ' .
The saturation concentration depends on a number of
reactionsinvolving ozone production and destruction
terms that, integrated over the pulse, result in no net
increase. Important ozone destruction processes include
fast reaction of excited singlet states with O3
+ O3
O('D) + 0 3
O('D)
(R62)
(25)
+20
(R65)
(26)
+0
+ 202 + 0
(R41)
(27)
(R15)
reactions with vibrationally excited molecules
(28)
+
OZ('Ag)+ 0
O*('Z;)
-+ 2 0 2
+0
0 3 +
O ~ ( V+) 0
The factor (1 - v) takes into account the fact that only
the energy not spent on ozone formation
is available
for heating the gas. Thesmall temperature drops in the
metal electrode and the
glass dielectric canbe neglected.
If T,, is the wall temperature fixed by the cooling circuit
we can write the average gas temperature Tg as
Tg= T,
11.1. A discrete model
3
2
202
3 +0 2
+ 0;
(R68)
(29)
as well as ozone decomposition by electron impact
e
+ O3+ e + O 2 + 0
(R8).
(30)
There exists no direct measurementof the cross section
or ratecoefficient for reaction R8. From the increaseof
the 'arcing voltage' with rising 0 , concentration in O,/
O3mixtures Samoilovich and co-workers [43] estimated
that the ratioof electron-impact dissociation rates of 0 ,
local temperature rise in a
11. Concentration build-up and saturation concentration
So far we have looked at the ozone production
of a
single micro-discharge in pureoxygen.We
will now
approach the problem of calculating the relative ozone
concentration x 3 = [O,]/ndue to asuccession of microdischarges.Withincreasingbackgroundozoneconcentration a number of additional reactions involving
O3 will becomeimportant.Theresult
is thatthe
efficiency of individual micro-discharges decreaseswith
rising background concentration.
1430
10-1
1
10
Speciftc energy ( e V / 0 2 )
Figure 14. The development of the ozone concentration as
a function of the specific energy.
Ozone synthesis from oxygen
and 0 2i.e.
, p s / p 7= 5. This value was also used
in model
calculations of Kastelewicz and Bachmann [44,45]. A
value of about 12 was inferred by Devins [l]and values
by Yagi and Tanaka
between 15 and 30 were determined
[2] from the interpretation of ozone measurements. In
reality, p s / p 7 will beafunction of E/n. Taking into
consideration the differenceof the dissociation energies
of O2 and O 3 and assuming that the electron impact
cross sections are otherwise equal one gets
P8 = P? exP(AEDlss/k~e)= P? exp(4lk7-e). (31)
This relation was used in [46]. At E / n = 110 Td this
gives a value of ps/p7= 4 which is probably the lowest
valueimaginable. As a first approximation we usea
value of ps/p7= 8 in our calculations for p 1 bar.
Infigure 15 we show the changes in the different
particle species during a pulse calculated at the saturation concentration. This pulse was generated by the
same electric field variation as the pulse in figure 10. To
demonstratetherelativeimportance
of thedifferent
processes we also plotted the contributions of the different ozone formation and ozone decomposition processes. The amount of ozone destroyed during the first
100 ns is exactly replenished during thefollowing 10 p .
It is apparent that a numberof processes determine the
saturation concentration. With our reaction schemewe
canroughlypredictthemeasuredsaturationvalues.
of additional
It is conceivablethattheintroduction
processes will slightly alter this balance. It should also
be pointed out that the ratio of activation energy over
on
temperature in reaction R11 has a large influence
the saturation concentration. Thisis the reasonwhy the
introduction of an elevated 'reaction temperature' [14161, or a reduction of the activation energy of reaction
R11 [24] can compensate for the omission of some of
the loss terms.
11.2. Continuous evaluation
general relation if we use this parameter as the independent variable. The efficiency of a micro-discharge
for a given electric pulse is a well defined function f ( x 3 )
of the background ozone concentration. Two situations
are of special significance:
(i) The first pulse in pure oxygen (x3= 0) with the
highest efficiency q l and
(ii) the saturation concentration x3 = x3swhere the
efficiency dropstozerobecausenonetozoneproduction results from this pulse.
The differential efficiency at the concentration
write as
(32)
= x3ofb3)
wheref(x3) is the normalised amountof ozone produced
during the kth pulse and x30is the ozone concentration
after thefirst pulse. The functionf(x,) has the boundary
valuesf(0) = 1 andf(x3J = 0. The functionf(x3) can be
calculated for anygiven pressure, temperature and E/n.
As figure 16 shows we getamonotonically,almost
linearly, falling curve.
To relatethis to measurable quantitieswe also introduce the integral efficiency q(x3)which is defined as the
total amount of ozone produced divided by the total
energy consumed or, as the mass flow of ozone at the
output divided by the power. Every volume element
enters the ozoniser at zero ozone concentration x3 = 0
and leaves it at a certain concentration
x 3 depending on
power and mass flow.
Disregarding the small changes of the electrical discharge conditions due to therising ozone concentration
we assume that the exit ozone concentration is builtup by identicalmicro-discharges of energy E l . The
efficiency of the first pulse is given by
r(x3 = 0 ) = X 3 0 / E 1
(33)
and the efficiency after an arbitrary numberof K pulses
=
r(x3) =(34)
X3/KE,.
The only parameter that changes during the passage of
avolumeelementthroughtheozoniser
is the rising
background ozone concentration. Thuswe can derive a
I
I
x 3 we
I
I
l
I.
l
0
10-8
10-6
Tlme i s )
Figure 15. The changes of different particle species in a
micro-discharge at the saturation limit.
0.2
06
10
Norrnallsed concentmtlon
Figure 16. Calculated differential f(x,) and integral g(x3)
efficiencies broken and full curves, respectively; and
comparison with measurements, open circles.
1431
Dl1
B Eliasson et a/
By inverting and integrating equation (32) we get
(35)
By inserting equation (35) into equation(34) and at the
same time considering equation (33) we get
material ( y , dielectric constant E , surface of dielectric)
or the feeding circuit (dE/dt) will mainly have an influence on the two important parameters, thesingle pulse
efficiency v , and the saturation concentration x3s. By
confronting our model to experimental datawe will see
that this is in principle the case.
12. Experimental techniques
which we write as
v(x3) = r&3)
(37)
The function
dX3)
= x3/Ji3 dx;/f(x;)
0
can be calculated once the pressure, temperature and
the reducedfield are specified. In figure 16 the calculated
g-function is also included and shows the familiar shape
of measured efficiency versus concentration curves of
ozonisers. Using the single pulse efficiency q l and the
saturationconcentrationtonormalisethe
axes we
get a fairly universal presentation of the functions f ( x 3 )
and g(x3) thatdependsonly
slightly onthechosen
parameters. In the expression in equation (37) we have
separated the physics of the discharge from the chemistry of theozonebuild-up.Thusthe
singlepulse
efficiency r l depends mainly on thephysical parameters
and the g-function comprises mainly the chemistry of
the ozoniser. This separation turns out very
to behelpful
when it comes to understanding what parametersinfluence the performance of an ozoniser. The conclusion
would then be that changing experimental conditions
( T , p ) in anozoniser, changing thegeometry ( d ) ,
The small plate ozoniser (figure 1) was used to study
individualmicro-discharges:Lichtenbergfigures,current pulses, transferred charge in a micro-discharge. A
number of experiments with different devices revealed
that experiments with such a relatively small electrode
area (7 cm X 7 cm) are not well suitedforaccurate
determination of integralparameters likemaximum
efficiency andsaturationconcentration.One
of the
reasons is certainly that the micro-discharges close to
the edge of the electrode are inherently different from
those surroundedby other micro-discharges. This
shows
up, for example, in reported saturation concentrations
[47] which are much smaller than those obtained under
the same conditionsin annular dischargegaps of reasonable length. With a
typical gap spacing of 1mm the
entrancelengthforthedevelopment
of the velocity
and temperature profiles will be of the order of a few
centimetres [42,48]. We, therefore, decided to use cylindrical ozonisers with annular gaps
of 0.3-5 mm spacing
and 0.3-1 m length (figure 17). The outer electrodewas
18/8) cylinder,the
provided by astainlesssteel(ST
temperature of which waskept constantby a thermostat
circuit using water. The inner electrode was provided
by an internal aluminum coating inside a Pyrex tubeof
1.8 mm wall thickness. The power was supplied by an
Figure 17. A cylindrical discharge tube with an annular gap. (A, glass tube; B, aluminum
coating; C, cooled stainless steel cylinder; D, Plexiglas end caps; E,high-voltage
transformer; F, AC power source; G, thermostat.)
1432
Ozone synthesis from oxygen
source(50-5000 Hz) and ahigh-voltage transformer (10-30 kV peak voltage). The power supplied
to the discharge tube was measured with an accurate
electronicpowermeter
of 20 kHzbandwidth.The
ozoneconcentration was determined in anexternal
absorption cell from absorption measurements at i\. =
253.7 nm close to the maximum of the Hartley absorptionband of ozone.Todeterminetheozoneconcentration we made use of the absorption cross section
U (253.65 nm) = 1.115 X 10"' cm2 published in [49].
AC power
13. Comparison with experiments
From a theoretical description of ozone formation in
dielectric barrier discharges one expects, besides predictions for the maximum attainable
efficiency and saturation
concentration,
a
modelling of the
major
experimental trends. The parameters that
have the largest influence onozone formation are gap spacing,
pressure and temperature.
13.1. Maximum efficiency
Our calculations (figure8) predict a maximumefficiency
of 33% corresponding to 0.22 O3 molecules per eV or
400 g ozone per k w h . This value can be reached only
if energylosses to ionscanbeavoided
and, atthe
same time, the oxygen atom concentration in a microdischarge
can
be
kept
under
From
figure 5 we
see that faint micro-discharges tend to have higher ion
losses. So it may not be possibleto meet both conditions
at the same time. Thehighest ozone yields we measure
at very low ozone
concentration
about
are
250 gkW-'h-l.Inpulsedozonisers
Salgeandcoworkers[50]obtainedabout
300 g kW" h". More
recently, Yamabe and co-workers [51] claimed ozone
yields in the rangeof 400450 g kW" h-l. These experiments were carried out with short discharge pulses in
oxygen/helium mixtures. It may also be of interest
to
point out that pulse
radiolysis with high-energy electrons
in oxygen [52] rendered ozone yields of 250 g kW" h"
a
comparable to that
(0.14 O3molecules per eV), value
obtained in ozonisers.
For arealistic comparisonof our measurements with
calculations we have to take into account the strength
of the micro-dischargesanditsvariation
with gap
spacing and pressure. It is characterised by the relative
atomconcentration x10 in amicro-dischargechannel
which is a function of the gas density n , the gap spacing
d andthe effectivereduced field (E/n),ff.Analytical
considerations of streamer breakdown at atmospheric
pressure lead to the relation xl0= Xlo (d/do) (n/n,J2,
where Xlo is a function of (Eln),, and do and n,, are
constants [24]. On the other hand, the determination
of
xIo from NOz admixtures(figure 13) leads to x,,,
(n/no). Furthermore, the measurements of the charge
Q, as a function of gap spacing (figure 2) lead to Q,
(d/do).In order to describe the gap and density
variation
of xlOby using the simplest model possible we assume
-
Figure 18. A comparison of measured and predicted
efficiency at low background ozone concentration
([O,]
= 0.3%). (-)
( A ) , 1 bar; (---), (0),
3 bar.
the following relation
x10
= flo(d/dn)(n/no)
(38)
where XIo= 1.8 x
do = 0.1 cm and no =
2.4 x
cm-3. In thissimplemodel
we neglectthe
E / n dependence of Xlo.
The calculations of § 6 showed that the
effective field
at current maximum can be considerably higher than
the field necessary for discharge initiation. In order to
include the field variation with gap spacing and pressure
we assumethatthe
effective field is 1.5 times the
Paschen field. This model (figure 18) predicts a maximum of the efficiency depending on gap spacing and
shifting towards narrower gaps at higher pressures. The
decreasetowardslargergapsandhigherpressures
is
caused by the increase of the atom concentration in a
micro-discharge. The fall-off towards narrower gaps is
due to an increase in the effective field strength. The
lie
experimental curves show the same tendency and
approximately 20% below the calculated values. Considering that the theoretical treatment starts from
basic
principles the agreement is remarkable. At thistime
it is notclear whetherthe smalldifferencebetween
calculation and measurement is due to inaccuracies of
loss mechthe cross sections used or whether additional
anisms have to be considered.
13.2. Saturation concentration
As we pointed outin 8 11 a numberof ozone destruction
processes determine the value of the saturation concentration. One of them, the destruction of ozone by
electron impact is not well known. In Q 11 we characterised this processby the parameterf= p 8 / p 7 ,the ratio
of the dissociation rate coefficients of 0, and 02.It is
obvious thatf depends on the electron energy and thus
also to some degree on gap spacing and pressure. In
order to model the saturation concentration as a function of pressure we have to introduce an assumption as
to how f varies with pressure. Assuming that f equals 8
for 0 S p 6 1 bar and rises linearly from
8 to 32 between
1433
B Eliasson et a/
destruction terms gain importance as compared to the
ozone three-body
process R9.
To test the model further we made the same meas,
_
urements
elevated
attemperatures
~
by_
increasing the
wall temperature.Ourmodelpredictsthesaturation
concentrationfor p 2 2reasonablywell,
while the
values at lower pressures are
slightly overestimated. But
again, we can state that the overall tendencies arefairly
well described by the model.
formation
16
14. Conclusion
I
0
4
I
1
2
I
I
3
p (bar1
Figure 19. A comparison of (0),(A)measured and (-)
calculated saturation concentration (gap spacing
d = 1 mm).
1 and 4 barresults in areasonable fit of themeasurements (figure 19). Our measurements are restricted
to pressures above 1 bar. The rising part of the saturation curve, however, is well documented by measurements of other authors [ l , 47, 531. In our model the
decrease of the saturation concentration towards
higher
pressure is mainly broughtabout by theassumed fvariation. The rising part, on the other hand, is partly
due to the rising electric field. But, more importantly,
it is due to thefact that at lower pressure the two-body
Ozone formation in dielectric barrier discharges can be
calculated from known electron collision cross sections
and published ratecoefficients. We have shown that our
model of the micro-dischargesin oxygen can predictthe
performance of ozonisersverywell.Itcouldalsobe
shown that ozoneis mainly formed directly from oxygen
atoms. These, in turn, are formed essentially by two
electronic dissociation processes of O 2 with threshold
energies of 6 and 8.4 eV. Energy losses to ions are
negligible under optimum ozoniser conditions. Excited
states have aninfluence on the maximumefficiency and,
evenmorepronounced,onthesaturationconcentration. Its value is alsoinfluenced by electronic collisions
resulting
in
ozone
destruction.
The
most
important parameter determining the performance
of
an ozoniseris the strengthof the micro-discharges which
can be characterised by theatomconcentrationproduced by amicro-discharge. Our modelincludesthe
physical and chemical aspectsin enough detail to predict
the theoreticallimits of ozone generation and the major
experimental trends.
Appendix. List of reactions
e + O2
e O2
e 00- M
0- + 0
0- + 0:
e O2
+
+
+
+
0 ; + 2e
-,o-+o
+
+O+2e
+ O + M + e
+02+e
+o+o,
+ o ( ~ P )+ O(3P) + e
+ O(3P) + O('D) + e
+ O + 0 2 + e
+ O('D) + O,('A,) + e
+0,+M
+O+O,+M
+ 202
+02+M
+ 02('Ag) + e
+O?+M
+ 0 2 + hv
+ 202 + 0
+ 2 0 2 + O('D)
203
-+02+e
-+03+e
+
+o;+o
1434
Ozone synthesis from oxygen
+ 0'
02('Ag)
0 O3
+
+o:+o
+
0- + 0 2 ( ' 2 i )
e + O2
O2(l2;) + M
0 2 ( l q
e + O
e + O2
0- + 0 2
+ O,('Z,f) + 0
+O+02+e
+ O2(lX;) + e
+02+M
+0 2
hv
+ 0' + 2e
+0++0+2e
2
+
+03+e
+O"cM
+ 0- hu
+ 0- + 0 2
+
+
O3 + wall
0- + 0 ; + M
0 + O('D) + M
hu + O3
O('D)
2
+o,+o
e + O + M
e + O
e O3
O('D)
O('D)
O('D)
+0
02('Ag)
+o,+o
+ products
+03+M
+02+M
+ O('D) + O2(lAg)
+
+M
o(3~)
+ o2
+ O + M
+O+hu
+0
02('2;)
+ 0 + 02(lAg)
+
+ O2
+ 0,
+
202
+20
02('Ag) + 0,
+ 0 2
+
e + 0 2 + M
e + O2
e+O;+M
e + 0:
+O;+M
+ 0;
hu
+02+M
+ 0 + O('D)
e+O++M
e O+
e + 02(lA,)
e + O2
+ O + M
+O+hu
-0: + M
+ O z ( u )+ e
+ 202 + 0
+ 02('29+)
+
+ 202 + hv
+ 202('Ag)
+O,+M
+
+0
0?('2gt)
+
+o+o
+M
3
202Wg)
O J q ) +0 2
01 + 0'
M
0 , + o+
0, + 0
+
0; + 0;
01 + 0 ;
OF
0;
07
+M
+M
+ 0,
+0
3
+ O,('Ag)
o++ 0 ,
e
+ 0 + 0 2
0- + 0 2
+O,+e
+ 202 + M
+ 202
+0 2 + 2 0
+02+M+e
+
+0 2
+0
3
0 +0 3
+ 0; + 0 2
+ 20, + e
-+ 0 ; + 0
+ 0; + M
+ 0; + M
+202+ e
+ OF + 0 2
+O++O+2e
+2
0, + 02(lAg)
0- + 0 3
0- + O 2 + M
e+03+M
0, + 0
0 2
+o;+o
(R191
(R20a)
(R20b)
(R21)
(R23a)
(R23b)
(R241
(R251
(R26a)
(R26b)
(R27a)
(R27b)
(R28a)
(R28b)
(R29)
(R301
(R311
(R32a)
(R32b)
(R33a)
(R33b)
(R34a)
(R34b)
(R35a)
(R35b)
(R35c)
(R36a)
(R36b)
(R37a)
(R37b)
(R37c)
(R38a)
(R38b)
(R391
(R40)
(R411
(R42a)
(R42b)
(R431
(R44a)
(R44b)
(R45a)
(R45 b)
(R46a)
(R46b)
(R46c)
(R471
(R48a)
(R48b)
(R491
(R501
0351)
(R521
(R53)
(R54a)
(R54b)
(R551
(R56)
1435
B Eliasson et a/
+ 0- + M
+ 0+ O*('C,+)
O++O+M
0 ; + O+
0; + M
e + O3
0'
Of
0;
e + O2
0 2 ( A '2;) + M
0 2 ( c 'E;) + M
0;
+o
+02+M
+20
+ 202
e
+Oz+M
+
+o,+o
+O,+e+M
- 0 ; +2e
-0: + O + 2 e
+O++O-+O+e
0 2 ( A 32:, . . .) + e
-0; + M
+ products
-
+o+o,
+ 0: + 0 2
+ 0 2 + 0;
-202
+0*+M
+O,+M
References
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