Oxygen-induced wavefront instabilities and disorder in the Belousov-Zhabotinsky reaction

Article abstract of DOI:10.1016/S0009-2614(98)00392-3

Wavefront instabilities leading to spatiotemporal disorder in a convection-free and horizontally homogeneous Ru(bpy)₃²⁺-catalyzed Belousov-Zhabotinsky reagent had previously been measured and simulated. Necessary conditions in a 20% O₂ atmosphere (air) were: high light intensities (I>150 mW/m²) and low catalyst concentrations (≤1 mM). Here, we show that at sufficiently high O₂ concentrations, comparable instabilities and disorder appear even in the dark or at high (≥1 mM) catalyst concentrations. In contrast, in the ferroin-catalyzed reagent such dynamic processes are not observed at any value of I in air, although they do occur - independently of I - at sufficiently high O₂ concentrations.

Full text of DOI:10.1016/S0009-2614(98)00392-3

5
June 1998
Chemical Physics Letters 289 Ž1998. 35–40
Oxygen-induced wavefront instabilities and disorder in the
Belousov–Zhabotinsky reaction
Mario Markus, Andr e´ Czajka
Max-Planck-Institut f u¨ r Molekulare Physiologie, Postfach 10 26 64, 44026 Dortmund, Germany
Received 12 February 1998; in final form 20 March 1998
Abstract
Wavefront instabilities leading to spatiotemporal disorder in a convection-free and horizontally homogeneous
2
q
RuŽbpy.3 -catalyzed Belousov–Zhabotinsky reagent had previously been measured and simulated. Necessary conditions in a
2
2
0% O2 atmosphere Žair. were: high light intensities ŽI)150 mWrm . and low catalyst concentrations Ž(1 mM.. Here,
we show that at sufficiently high O concentrations, comparable instabilities and disorder appear even in the dark or at high
2
Ž01 mM. catalyst concentrations. In contrast, in the ferroin-catalyzed reagent such dynamic processes are not observed at
any value of I in air, although they do occur — independently of I — at sufficiently high O2 concentrations. q 1998
Elsevier Science B.V. All rights reserved.
1
. Introduction
low spatial correlations w12x. The novelty of this
spatiotemporal disorder was that it appeared in the
absence of hydrodynamic flow or horizontal inhomo-
geneities.
Manipulations of wave patterns by light have
been extensively studied using the RuŽbpy. 32 q-cata-
lyzed Belousov–Zhabotinsky ŽBZ. reaction w1–11x.
In particular, we found wavefront instabilities lead-
ing to spatiotemporal disorder for high light intensi-
We found that our observations are only possible
in the presence of a catalytic gel covered by a
non-catalytic solution. Taking this into consideration,
we proposed a mechanism for the formation of rip-
ples and for their breakdown w14x. This mechanism is
a modification of a model by Kuramoto w15x who
assumed that fluctuation valleys are retarded Žand
thus amplified. by the fact that the inhibitor Žhere
2
q
ties I and a low Ru concentration Ž0.71 mM.. The
observed modes — which lasted up to 1.5 h —
2
were: ‘ripples’ for 150-I-400 mWrm and wave
breaking in the ripple-valleys leading to labyrinthine
structures and a mode we called ‘frazzle gases’ for
larger I w12x. The occurrence of ripples was shown to
y
Br . in the waveback smoothens out faster than the
be related to a non-monotonic eikonal relationship:
the normal wavefront velocity increases on increas-
ing wavefront curvature K within an interval around
Ks0, whereas it decreases elsewhere w13x. The
frazzle gases consisted of wave fragments that grew,
broke and annihilated by collisions with each other,
sustaining a global disordered state with relatively
activator Žhere HBrO . in the wavefront, thus caus-
2
ing the inhibitor to get ahead of the front of the
activator valley. This idea is not straightforwardly
applicable to our case because of the fast and almost
y
irreversible HBrO –Br annihilation, so that the
2
y
assumption of Br tunneling through HBrO is un-
realistic. In our model w14x we let Br surpass
2
y
0
009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved.
PII: S0009-2614Ž98.00392-3

3
6
M. Markus, A. CzajkarChemical Physics Letters 289 (1998) 35–40
Fig. 1. Spatiotemporal modes measured for the RuŽbpy. 32 q-catalyzed BZ reaction in environments of varying O2 concentrations and for
varying light intensities. Catalyst concentration: 0.71 mM. S, stable Žsmooth. wavefronts; R, ripples; F, frazzle gases; E, wave extinction.
HBrO2 via a detour over the upper non-catalytic
solution. Retardation — leading to amplification and
in extreme cases to wave breakup — of fluctuation
et al. w18x measured the period and amplitude of
temporal oscillations increasing, upon increasing the
illumination.
y
valleys occurs by Br concentration enhancement
In addition, the BZ reaction has been shown to be
due to the concave geometry, which implies converg-
ing vectors of diffusive flow of Br . Cellular au-
tomata simulations based on this model and on an
isotropic quasi-stochastic geometry w16x reproduce
well the visual impression of the measured modes, as
well as their quantification by autocorrelation analy-
sis and by the determination of the eikonal relation-
ship w14x.
sensitive to molecular oxygen. O2 inhibits
y
2q
RuŽbpy.3 -catalyzed oscillations even in the dark
w19x. For the ferroin-catalyzed reaction, spatially in-
homogeneous O causes refraction and reflection of
2
chemical waves w20x, comparable to the effect of
‘chemical lenses’ w21x, which were constructed using
light inhomogeneities. For the cerium-catalyzed reac-
tion, O lowers the activation enthalpy and entropy
2
However, the ferroin-catalyzed BZ reaction has
also shown to be light-sensitive. Miyagawa et al. w17x
induced spatial patterns by light projections. G a´ sp a´ r
w22x, causing changes in the oscillations, such as
enhancements of the induction time and the period
w22,23x.
Fig. 2. Ripples measured for wRuŽbpy.2qxs0.71 mM and 50% O in the ‘dark’ Žlowest possible light intensity: Is2 mWrm .. Ža. ts0;
2
3
2
Žb. ts4.9 min.

M. Markus, A. CzajkarChemical Physics Letters 289 (1998) 35–40
37
Considering the apparently related inhibitory ac-
tion of light and O , Krug et al. w24x formulated a
2
modified Oregonator model, in which O and light
2
y
are considered together in one single Br -generating
parameter. However, it has remained an open ques-
tion as to whether this is just an algorithmic simplifi-
cation or if it has a well-founded mechanistic back-
ground. The intention of the present work is to
broaden our view on the action of oxygen, as com-
pared to that of light, by investigating experimentally
the role of these two agents in the occurrence of
wavefront instabilities and disorder.
2
. Materials and methods
Both the RuŽbpy. 32 and the ferroin-catalyzed
q
reactions were started by pouring a 3.1 ml solution
Ž0.18 M NaBr, 0.33 M malonic acid, 0.39 M NaBrO3
and 0.69 M H SO in water. into a Petri dish on the
2
4
same volume of gel Žheight: 0.9 mm. containing the
immobilized catalyst. The temperature was held at
2
58C. White light from a 250 W halogen lamp first
passed an interference filter Ž450.6 nm for experi-
ments with the Ru-complex and 490 nm for the case
of ferroin., then a diffusion screen, then the Petri
dish, and then the video equipment. The gel was
used to avoid hydrodynamic flow, which by itself
causes disorder as it interacts with chemical waves
w25,26x. For the preparation of the gel, see Ref. w27x.
2
q
Fig. 3. Frazzle gas measured for wRuŽbpy. xs0.71 mM, 70%
3
For comparison with our former results, all experi-
ments concerning the influence of light on the
O2 in the ‘dark’ ŽIs2 mWrm.. Ža. ts0; Žb. ts10 s; Žc. ts20
s.
2
q
RuŽbpy.3 -catalyzed reagent were conducted in the
same way as in Ref. w12x.
In order to study the influence of oxygen, the
apparatus was extended by putting the Petri dish in a
box ŽVs1.45 l, with a transparent bottom and top.
3
. Results
through which we streamed an N –O mixture com-
2
2
ing from a gas mixing pump ŽW o¨ sthoff DIGAMIXM
From experiments under different O2 and light
3
00ra; 0.75 lrmin; 1% O — concentration error;
intensities I, we constructed the diagram given in
2
2
q
measurements were performed after a transient of 10
min.. In all experiments, the initial condition was a
Fig. 1 for the Ru Žbpy.3 -catalyzed reaction. We see
in this case that — at least qualitatively — light and
spiral pair extending over the whole Petri dish, which
was allowed Žas in Ref. w12x. to develop for 2 h in air
in the dark.
O have analogue effects. The ripple and frazzle gas
2
regimes for air Ž20% O , y-axis of Fig. 1. have been
2
pictured and analyzed in previous works w12,13x. We

3
8
M. Markus, A. CzajkarChemical Physics Letters 289 (1998) 35–40
illustrate here the effect of high oxygen concentra-
light intensity and oxygen concentration are suffi-
2
q
tion in Fig. 2 Žripples. and Fig. 3 Žfrazzle gas. at
ciently large. In fact, we obtained Žat wRu xs6
2
4
Is2 mWrm , which is the intensity below which
mM and 100% O . ripples for 3.2=10 -I-5.4=
2
4
2
4
no measurements were possible and which we thus
10 mWrm and frazzle gases for 5.4=10 -I-
4 2
define as ‘darkness’ Ž x-axis of Fig. 1.. Note that this
7.1=10 mWrm . ŽWaves extinguished at higher
I.. These large I values could only be obtained by
removing the interference filter between the lamp
and reagent and instead placing it between the reagent
and video camera. We denote this by placing an
I is much lower than the lowest values given by
other authors; this is because we determined the
intensity after light had passed the interference filter.
For the Ru catalyst, we observe that the whole
light-dependent scenario, as described in Ref. w12x,
appears — with the same dynamic modes — as an
oxygen-depending scenario in the dark. As for fraz-
zle gases, Fig. 3 illustrates the typical overall be-
haviour of this mode: growth of wave fragments is
compensated by breaks and Ždestructing. collisions
)
2q
asterisk on I ŽI .. The results for large wRu x at
100% O are given in Fig. 4b.
2
For the ferroin-catalyzed reagent in air Ž20%. —
in contrast to the Ru reagent — we did not observe
any instabilities or disorder Žsuch as ripples and
frazzle gases., but only stable wavefronts in the
whole range of catalyst concentrations Ž-6 mM.
so that an average global disorder is maintained, the
mode somehow resembling a gas at a microscopic
scale.
4
2
and of I Ž-7.1=10 mWrm . that were used in
the experiments with the Ru complex Žsee above and
Ref. w12x.. This is a remarkable finding considering
In Figs. 1–3, wRu2 xs0.71 mM. Previously w12x,
q
we had stated that spatial disorder is only possible at
that sensitivity of the ferroin-catalyzed reagent to
visible light had been found in other experimental
situations w17,18x. However, we did obtain disor-
2
q
extremely low wRu x, as compared to the concentra-
2
q
tions used in other works ŽwRu xs2.5–4 mM.. We
can now state that this is not valid if light is replaced
dered modes with ferroin at sufficiently high O . In
2
by O . In fact, we get ripples in the dark for
fact, for wferroinxs0.71 mM, ripples appeared for
2
2
2
q
wRu xs3 mM if O2 is between 77% and 100%
O between 61% and 80% and frazzle gases between
Žsee Fig. 4a..
80% and 88%. ŽWaves extinguished for larger O ..
2
Ripples and frazzle gases are also possible for
even higher wRu x Žup to 6 mM. provided both the
Under these conditions the ripple amplitude was
small. For a better exemplification we thus show
2
q
Fig. 4. Ža. Spatiotemporal modes of the Ru-catalyzed reaction measured in environments of varying O concentrations Žordinate. and
2
2
varying catalyst concentrations Žabscissa. in the ‘dark’ ŽIs2 mWrm .. S, stable wavefronts; R, ripples; F, frazzle gases; E, wave
extinction. Žb. Modes at 100% O for varying light intensities Žordinate. and catalyst concentrations Žabscissa.. I ) : light intensity from the
2
lamp, i.e. without passing an interference filter.

M. Markus, A. CzajkarChemical Physics Letters 289 (1998) 35–40
39
Fig. 5. Modes for the ferroin-catalyzed reaction at 100% O . Ža. Ripples for wferroinxs2 mM; Žb. frazzle gas for wferroinxs1.4 mM.
2
ripples in Fig. 5a for a higher wferroinx, namely 2
mM ŽO is 100%.. Frazzle gases Žfor the same O .,
HBrO2 in one case w28x and bromomalonic acid
ŽBrMA. in the other w29x.
2
2
appearing at wferroinxs1.4 mM are shown in Fig.
For the action of O , measurements by Ram
2
5
b. The transitions between modes involving ferroin
Reddy et al. w30x point to the following mechanism:
were independent of I in the I range considered
above. Besides the fact that the excited wavefronts
are broader for ferroin under these conditions, the
disordered modes are similar to those in the Ru
reagent.
)
2q
bpy.3 qOy2
2q
Ru
Ž
bpy.3 qO lRu
Ž
Ž .
2
2
y
q
2O q2H ™H O qO
Ž .
3
Ž .
4
2
2
2
2
y
q
y
BrO q3H O q6H ™Br q3H Oq3O
3
2
2
2
2
This mechanism poses an open question if one
considers the above reported observations of O2
action in the dark; in that case, the photochemical
excitation necessary for reaction Ž2. may be too low.
4
. Discussion and outlook
For the RuŽbpy. 32 q-catalyzed reaction we have
y
To account for the independence of irradiation, Br
shown that — at least qualitatively — O and light
may be produced by O2 in a way related to a
mechanism occurring in the cerium-catalyzed reac-
tion. In this mechanism, the peroxymalonyl radical
ŽMAOO . and the malonyl radical ŽMA . arise and
decay by virtue of the following reactions w31x:
2
have the same destabilization properties. The good
agreement of former w12,13x and present observations
with our simulations w14x confirms that both light
Ø
Ø
y
and O2 induce Br release. In fact, our model
includes a light- or oxygen-dependent production of
4
q
3q
Ø
q
y
Ce qMA™Ce qMa qH
Ž
Ž
Ž
Ž
Ž
5
6
7
8
9
.
.
.
.
.
.
.
Br , which decimates the activator HBrO in the
2
y
Ø
Ø
upper regions, thus facilitating the passage of Br
MA qMA ™H
MA qO ™MAOO
MAOO qMA™MAOOHqMA
via the upper solution. For the action of light, the
following mechanism w1x has been proposed:
Ø
Ø
2
Ø
Ø
6)
2q
y
q
Ru
Ž
bpy.3 qBrO q6H
2
4
q
3q
Ø
q
MAOOHqCe ™Ce qMAOO qH
MAOO qMAOO ™TAqMOAqO
MAOOH™P
3
q
y
™
6Ru
Ž
bpy.3 q3H OqBr
where RuŽbpy.3 is a photochemically excited
1
Ž .
2
Ø
Ø
Ž
Ž
10
11
2
)
2q
state. Two alternative mechanisms that have been
)
2q
proposed also involve RuŽbpy.
as a reducing
MA, TA, MOA, ETA and P are malonic acid,
tartronic acid, mesoxalic acid, 1,1,2,2-ethanetetra-
carbonic acid and unspecified products, respectively.
3
y
agent for the production of Br , the source of bro-
mide not being bromate, as in reaction Ž1., but

4
0
M. Markus, A. CzajkarChemical Physics Letters 289 (1998) 35–40
w7x M.K. Ram Reddy, M. Dahlem, V.S. Zykov, S.C. M u¨ ller,
Chem. Phys. Lett. 236 Ž1995. 111.
In the presence of BrMA, the transiently produced
Ø
y
MA could release Br as follows w32x:
w8x S. Grill, V.S. Zykov, S.C. M u¨ ller, J. Phys. Chem. 100 Ž1996.
Ø
Ø
MA qBrMA™MAqBrMA
Ž
Ž
12
13
.
.
1
9082.
Ø
Ø
y
q
9
w x
V. Petrov, Q. Ouyang, G. Li, J.L. Swinney, J. Phys. Chem.
00 Ž1996. 18992.
BrMA qH O™TA qBr qH
2
1
Thus, the action of O2 may be mechanically
different to that of light, although lumping both
effects into one parameter could be used as a compu-
tational approximation w12,24x. In addition, one
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79 Ž1997. 1941.
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should be cautious about the application of reaction
1
233.
Ž1. to the ferroin reagent Žas in Ref. w17x., since we
observed that the waves in the Ru reagent may be
destabilized equally well by O2 and light, while
those in the ferroin reagent are only destabilized by
w14x M. Markus, T. Schulte, A. Czajka, Phys. Rev. E 56 Ž1997. 1.
w15x Y. Kuramoto, Chemical Oscillations, Waves and Turbulence,
Ch. 7 ŽSpringer, Berlin, 1984..
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O Ža study with light-sensitized ferroin in the pres-
2
Ž
.
Soc. Jpn 64 1995 3105.
ence of methanol w33x or at extremely high ferroin
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43.
w19x M.K. Ram Reddy, Zs. Nagy-Ungvarai, S.C. M u¨ ller, J. Phys.
can conclude that if destabilization occurs at all, then
the qualitative macroscopic scenarios involving rip-
ples, frazzle gases and extinction, are similar for
ferroin Žby the action of oxygen. and the Ru com-
plex Žby the action of oxygen or light..
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1
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Acknowledgements
We thank the Deutsche Forschungsgemeinschaft
w25x K.I. Agladze, V.I. Krinsky, A.M. Pertsov, Nature 308 Ž1984.
ŽGrants Ma 629r4-2 and Ma 629r4-3., as well as
the Engel-Stiftung, Marl for financial support. We
also thank Ralf Girnus for image data processing and
for fruitful discussions.
8
34.
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5
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