pH Oscillations and complex reaction dynamics in the non-buffered chlorite-thiourea reaction

Article abstract of DOI:10.1016/j.cplett.2004.05.030

The concentration of hydrogen ions is found to evolve periodically in the non-buffered chlorite-thiourea reaction. Period-doubling, homoclinic and quasiperiodic bifurcations have been uncovered in this study. Experiments further illustrate that under the

Full text of DOI:10.1016/j.cplett.2004.05.030

Chemical Physics Letters 391 (2004) 349–353
www.elsevier.com/locate/cplett
pH Oscillations and complex reaction dynamics in the
non-buffered chlorite–thiourea reaction
a,b
Qingyu Gao , Jichang Wang
a,
*
a
Department of Chemistry and Biochemistry, The University of Windsor, ON N9B 3P4, Canada
b
College of Chemical Technology, China University of Mining and Technology, Xuzhou 211008, PR China
Received 23 February 2004; in final form 11 May 2004
Available online 1 June 2004
Abstract
The concentration of hydrogen ions is found to evolve periodically in the non-buffered chlorite–thiourea reaction. Period-
doubling, homoclinic and quasiperiodic bifurcations have been uncovered in this study. Experiments further illustrate that under the
reaction conditions employed in this investigation reducing the reaction temperature favors the occurrence of complex pH oscil-
lations. These experimental results provide new insight into the underlying mechanism of the chlorite–thiourea reaction, in par-
ticular regarding the significance of the nonlinear oxidations of sulfur(-II) compounds.
Ó 2004 Published by Elsevier B.V.
1
. Introduction
linear oxidations of sulfur-containing compounds or
nonlinear reactions of chlorite play the dominant role in
the above reaction. In particular, R ꢀa bai and Orb ꢀa n [13]
had successfully developed a general model to account
for oscillations occurred in chlorite-based oscillators.
The reason that no pH oscillations had been recorded in
the chlorite–thiourea reaction could simply be due to the
fact that the vast majority of existing investigations have
been conducted in the presence of buffer solution. Note
that the presence of a buffer appears to be essential for
the oscillatory phenomena in the chlorite–thiourea sys-
tem according to earlier investigations. To examine our
hypothesis and decipher the underlying reaction mech-
anism, in this study we investigated the dynamics of the
thiourea–chlorite reaction in the absence of any buffer.
As shown in the following, the concentration of hy-
drogen ions does exhibit periodic variation in the un-
buffered chlorite–thiourea solution. In addition, three
types of bifurcation routes leading to irregular pH
oscillations have been observed.
The sulfur chemistry is important in various areas such
as in energy industries [1], where improving the sulfur
abatement is desired, and in physiology [2], where sulfur
chemistry could be used to rationalize the physiological
role of sulfur-based amino acids. As an important sulfur-
containing compound, thiourea has attracted particular
attention in the last two decades. Oxidation reactions of
thiourea with chlorite have been found to support vari-
ous nonlinear dynamical phenomena such as periodic
and homoclinic chaotic oscillations, co-existence of two
limit cycles, and traveling waves [3–5]. Recent investiga-
tions by Epstein, Simoyi and their co-workers have sug-
gested that the oxidation of sulfur(-II) to sulfate is the
main reaction driving these nonlinear behaviors in the
chlorite–thiourea reaction [6–8]. However, in contrast to
other sulfur(-II)-based oscillators in which periodic
variations in the concentration of hydrogen ions have
been frequently observed [9–12], no pH oscillations have
been reported in the chlorite–thiourea system.
The absence of pH oscillations in the chlorite–thio-
urea reaction creates an uncertainty on whether non-
2. Experimental
*
Sodium chlorite used in this study was purchased
from Aldrich (ca. 80%) and was recrystallized twice
Corresponding author. Fax: +1-519-973-7098.
E-mail address: jwang@uwindsor.ca (J. Wang).
0
009-2614/$ - see front matter Ó 2004 Published by Elsevier B.V.
doi:10.1016/j.cplett.2004.05.030

350
Q. Gao, J. Wang / Chemical Physics Letters 391 (2004) 349–353
from 75% acetone–water solution in the temperature
range between )20 and 30 °C reaching a purity >99%
when determined by the iodometric titration. Perchloric
acid, thiourea and sodium carbonate were reagent grade
and were used without further purification. Solutions
were all prepared on daily basis by dissolving proper
amounts of reactants in the deionized water (ultrafil-
tered from Milli-Q (Millipore) system). All experiments
presented here were conducted in a continuous flow
stirred tank reactor (CSTR) thermostated through a
circulating water bath. The Plexiglas reactor has a vol-
ume of 28 ml. Solutions of sodium chlorite, thiourea and
perchloric acid were separately transferred to the reactor
by an ISMATIC high precision peristaltic pump (Swit-
zerland). The pH and Pt potential were simultaneously
followed with a glass electrode and a platinum electrode,
respectively, coupled with a HgjHg2SO4jK2SO4 refer-
ence electrode. Signals from the reaction were recorded
by an IBM PC through a Powerlab/4sp (ADInstru-
ments, Australia).
flow mixture into the barium chloride solution where
precipitations took place due to the presence of sulfate
ions. Such an observation is consistent with recent
studies done by Simoyi [8] and by Margerum [15], which
illustrated, respectively, that the oxidation of thiourea
produced oxysulfur(IV) compounds and the reaction of
chlorite and S(IV) was auto-catalyzed by hydrogen ions.
The above investigation, together with existing liter-
ature [6–8,16], suggest that the observed pH oscillations
arise from sulfur(-II) oxidations, where the increase and
decrease in the pH are resulted from S(-II) to S(0) and
from S(0) to S(VI), respectively. To maintain the oscil-
latory cycle, however, proper reaction conditions in-
cluding the background pH value, flow rates, and
[NaClO ]/[SC(NH ) ] ratio must be satisfied. Qualita-
2
2 2
tively, variations in the pH of the reaction solution
could be accounted based on the following three steps:
þ
ꢀ
1. H +ClO +SC(NH2)2 !HOCl+HOSC(NH)(NH2)
2
ꢀ
2ꢀ
+
4
2. H2O + HOCl + ClO + HOSC(NH)(NH2) ! SO
2
2Cl + OC(NH2)2 + 3H
ꢀ
þ
þ
þ
3
. OC(NH2)2 + H2O + 2H ! 2NH + CO2
4
Reactions 1 and 3 shall cause an increase in the pH
þ
via directly consuming H or producing a weaker acid.
To induce the decrease in pH, process 2 produces
3
. Results and discussion
þ
þ
H
via an autocatalytic cycle catalyzed by H . The
Fig. 1 presents a time series of pH oscillations ob-
production of the sulfenyl acid has been found to be
autocatalytic through the formation of dithiobisform-
amidine [6]. The overall stoichiometric reaction can be
expressed as:
tained in the non-buffered chlorite–thiourea reaction.
Here, the system oscillates between pH 2.5 and 2.8, in-
dicating that variations in the concentration of hydro-
gen ions are at the order of 10 3 M. Such a magnitude is
significantly larger than those reported in most of the
sulfur-containing oscillators [12]. Note that keeping the
pH of the reaction mixture below 3.0, a condition close
to the pKa of HClO2 [14], is desired here because Cl(-III)
is found to exhibit stronger oxidation ability under such
an environment. A sharp drop in the pH, a character-
istic of autocatalytic reactions, was found to be ac-
companied by the rapid production of sulfate ions,
which was identified by immediately injecting the out-
ꢀ
ꢀ
2
2ClO þ SCðNH Þ þ 2H O
2
2
2
2ꢀ
ꢀ
þ
¼
SO þ 2Cl þ 2NH þ CO
2
4
4
þ
Despite the production of NH –NH and H CO –
3
2
3
4
HCO pairs, which consequently function as buffers to
ꢀ
3
minimize modulations in the concentration of hydrogen
ions, pH oscillations in the magnitude of 0.01–0.3 have
been recorded over a broad range of reaction condi-
tions. Variations in the reaction behavior with respect
to the change of flow rate are presented in Fig. 2. The
time series presented here were recorded through a
platinum electrode. These Pt potential oscillations are
anti-phased to the corresponding pH oscillations. Such
an anti-phased relationship between the pH oscillations
and oscillations in the Pt potential is the same as ob-
served in a batch reactor [16]. In Fig. 2, the following
2
2
2
.9
.7
.5
sequence could be identified: Period-1 (a) ! Period-2
2
(
(
b) ! Period-4 (c) ! Period-8 (d) ! chaos (e) ! 1
3 n
f) ! 1 (g) ! 1 (h), where the superscript indicates the
0
1000
2000
total number of small peaks per cycle. As the flow rate
is increased from (a) to (h), the system exhibits transi-
tions from period-doubling to homoclinic bifurcations.
When the flow rate is increased further, the system
evolves to a non-oscillatory steady state. A summary of
the bifurcation diagram as a function of the flow rate is
presented in Fig. 3.
time/s
Fig. 1. Time series of pH oscillations in the chlorite–thiourea reaction
ꢀ1
conducted in a CSTR. The flow rate equals 8.93 ꢁ 10ꢀ
3
s and the
reaction temperature is 45 °C. Initial concentrations of the reaction
ꢀ3
ꢀ3
mixture are [NaClO2]0 ¼ 2.0 ꢁ 10
mol/l, [SC(NH2)2]0 ¼ 1.5 ꢁ 10
mol/l, and [HClO4]0 ¼ 6.0 ꢁ 10ꢀ mol/l.
4

Q. Gao, J. Wang / Chemical Physics Letters 391 (2004) 349–353
351
(
a) 250
50
(b) 250
1
1
50
5
0
50
0
0
500
1000
1500
0
0
500
1000
(
c) 250
50
(d) 250
150
1
5
0
50
500
1000
1000
2000
(
(
e) 250
50
(f) 250
150
1
5
0
50
0
0
1000
500
2000
0
0
500
1000
g) 250
50
(h) 250
150
1
5
0
50
1000
500
1000 1500
time/s
time/s
Fig. 2. Time series showing transitions from period-doubled oscillations at low flow rates to mixed-mode oscillations at high flow rates. Reaction
conditions are [NaClO2]0 ¼ 2.10 ꢁ 10ꢀ mol/l, [SC(NH2)2]0 ¼ 1.20 ꢁ 10 mol/l, and [HClO4]0 ¼ 2.0 ꢁ 10 mol/l and T ¼ 45 °C. Flow rate k0 is
3
ꢀ3
ꢀ4
ꢀ
4
ꢀ1
ꢀ3 ꢀ1
ꢀ3 ꢀ1
ꢀ3 ꢀ1
ꢀ3 ꢀ1
ꢀ3 ꢀ1
s , (g)
adjusted as the following: (a) 5.36 ꢁ 10
ꢀ3 ꢀ1
s
s
, (b) 1.07 ꢁ 10
s
, (c) 1.25 ꢁ 10
s
, (d) 1.26 ꢁ 10
s
, (e) 1.30 ꢁ 10
s
, (f) 2.32 ꢁ 10
ꢀ
3
ꢀ1
2.67 ꢁ 10
s
, and (h) 8.04 ꢁ 10
.
P8
2
3
4
n
P1
P2
P4 chaos
1
1
1 -1
0
.40
0.81
1.17 1.25 1.267 1.48
2.32
2.68
3
-1
k
0
×10 s
Fig. 3. Bifurcation diagram showing the dependence of reaction dynamics on the flow rate. Concentrations of the stock solutions are the same as
those in Fig. 2.
In addition to the period-doubling and homoclinic
bifurcations shown in Fig. 2, quasi-periodic bifurca-
tions have also been obtained in the system. Fig. 4
presents two time series of quasiperiodic oscilla-
tions, which are achieved at the conditions [Na-
here. Our experiments illustrate that adjusting the re-
action temperature induces transitions between different
oscillatory modes. In general, raising the reaction tem-
perature also causes a decrease in the average value of
pH. Meanwhile, the frequency of oscillations is also
increased. Fig. 5a presents an example showing a tran-
sition of different mixed-mode oscillations as the result
of increasing the reaction temperature from 45 to 50 °C.
Again, under the same set of initial concentrations, a
decrease in the reaction temperature (45–40 °C) would
lead to a transition from period-1 (simple) to period-2
(complex) oscillations indicating that the low reac-
tion temperature favors the development of complex
dynamics.
ꢀ
3
ꢀ3
ClO2]0 ¼ 1.70 ꢁ 10
mol/l, [SC(NH2)2]0 ¼ 1.2 ꢁ 10
ꢀ
4
mol/l and [HClO4]0 ¼ 6.0 ꢁ 10
mol/l. As shown in
this figure, when the flow rate is increased from 8.5 ꢁ
ꢀ
4
ꢀ4 ꢀ1
s , the quasiperiodic oscillations
1
0
to 9.5 ꢁ 10
become less pronounced, indicating that a reverse
quasiperiodic bifurcation shall take place at a higher
flow rate.
The influence of reaction temperature on the above
complex pH oscillations has also been characterized

352
Q. Gao, J. Wang / Chemical Physics Letters 391 (2004) 349–353
4
. Conclusions
Although the chlorite–thiourea system initially con-
sists of only two components, various complex dynam-
ical behaviors including three types of bifurcation
sequences have been observed here. Such rich nonlinear
phenomena may arise from the fact that both of the
initial reactants, i.e., chlorite and thiourea, are capable
of building up oscillating reaction cycles. R ꢀa bai and
Orb ꢀa n had proposed a general model for the chlorite-
based oscillators in an attempt to explain the general
nonlinear behavior observed in reactions involving
chlorite ions and significant progress has been achieved
in their study [13,17]. However, the R ꢀa bai–Orb ꢀa n model
did not account for the possible pH dynamics from the
oxidation of S(-II) species and also failed in describing
the birhythmicity appeared in the chlorite–thiourea re-
action. Working from a different approach, Thompson
and co-workers [16] developed a general model on the
basis of the redox reactions of sulfur compounds while
the nonlinear kinetics from the chemistry of chlorite has
been completely omitted. The general model proposed
by Thompson and co-workers predicted the existence of
pH oscillations in the chlorite–thiourea reaction. The
observation of pH oscillations in this study provides
experimental supports to the sulfur(-II)-based reaction
mechanisms suggested in recent studies [6–8,16]. How-
ever, whether chlorite-based nonlinear kinetics also
plays a significant role in the thiourea–chlorite oscilla-
tor, in particular in the appearance of complex pH os-
cillations, remains to be understood. A hypothesis is
that, depending on the reaction conditions such as the
relative initial concentration of chlorite and thiourea,
the chlorite–thiourea reaction could be governed by
three different mechanisms, i.e., chlorite-driven, sulfur-
driven, and the co-existence of chlorite- and sulfur-dri-
ven mechanisms. Numerical simulations by considering
the co-existence of chlorite-driven and thiourea-driven
oscillations will be carried out in our future study.
Fig. 4. Quasiperiodic oscillations in the chlorite–thiourea reaction. The
ꢀ1
flow rate k0 is (a) 8.5 ꢁ 10ꢀ
4
s
and (b) 9.5 ꢁ 10ꢀ4
s .
ꢀ1
(
a) 2.36
.3
2
2
2
.24
.18
4
5-> 50˚C
0
400
800
1200
time/s
(
b) 2.31
Acknowledgements
The authors would like to thank Prof. Thompson and
Dr. Frerichs for helpful discussions. We would also like
to thank financial supports from Chinese Education
Ministry for the international exchange program to
GQY, NSFC (20103010) and EYTP of China, and the
National Science and Engineering Research Council
4
5 ->40˚C
2
2
.26
.21
0
2000
4000
6000
time/s
(NSERC), Canada.
Fig. 5. Transitions between different modes of oscillations induced by
adjusting the reaction temperature: (a) 45 ! 50 °C at flow rate
ꢀ
ꢀ
3
4
ꢀ1
References
k0 ¼ 5:367 ꢁ 10
k0 ¼ 4:460 ꢁ 10
s
and (b) 45 ! 40 °C at the flow rate
ꢀ1
s
.
Other reaction conditions are: [Na-
ꢀ
3
mol/l, [SC(NH2)2]0 ¼ 1.20 ꢁ 10ꢀ3 mol/l and
ClO2]0 ¼ 2.19 ꢁ 10
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4
[
HClO4]0 ¼ 5.0 ꢁ 10 mol/l.

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