Influence of external electric fields on reaction fronts in the iodate-arsenous acid system

Article abstract of DOI:10.1021/jp001157g

The propagation of arsenous acid-iodate reaction fronts of different net stoichiometries in externally applied dc electric fields is studied for a range of both electric field intensities and initial compositions of the reacting mixture (represented by the stoichiometric factor S₀). Regions of three different types of net stoichiometry in the parametric space E/V vs S₀, where E is the intensity of the applied electric field and V the reaction front propagation velocity, are determined both experimentally and by analyzing a reaction-diffusion-migration model that includes a realistic kinetic scheme of the reaction studied. Both agreement with and discrepancies between the theoretical predictions and experimental findings are discussed.

Full text of DOI:10.1021/jp001157g

9136
J. Phys. Chem. A 2000, 104, 9136-9143
Influence of External Electric Fields on Reaction Fronts in the Iodate-Arsenous
Acid System
Lenka Forsˇtova´,† Hana Sˇevcˇ´ıkova´,*,‡ Milosˇ Marek,† and John H. Merkin§
Department of Chemical Engineering and Center for Nonlinear Dynamics of Chemical and Biological Systems,
Prague Institute of Chemical Technology, Technicka 5, 166 28 Prague 6, Czech Republic, and
Department of Applied Mathematics, UniVersity of Leeds, Leeds, LS2 9JT, U.K.
ReceiVed: March 28, 2000; In Final Form: July 5, 2000
The propagation of arsenous acid-iodate reaction fronts of different net stoichiometries in externally applied
dc electric fields is studied for a range of both electric field intensities and initial compositions of the reacting
mixture (represented by the stoichiometric factor S0). Regions of three different types of net stoichiometry in
the parametric space E/V vs S0, where E is the intensity of the applied electric field and V the reaction front
propagation velocity, are determined both experimentally and by analyzing a reaction-diffusion-migration
model that includes a realistic kinetic scheme of the reaction studied. Both agreement with and discrepancies
between the theoretical predictions and experimental findings are discussed.
1. Introduction
electrophoresis fronts and fronts in which there is a much
enhanced reaction rate.
Applying electric fields can have a profound effect on waves
(pulses or fronts) propagating in ionic chemical systems. The
extensive experimental observations of reactors based on the
Belousov-Zhabotinsky (BZ) reaction have identified wave
acceleration and deceleration, including wave annihilation,1,2 as
well as the reversal in the direction of wave propagation and
wave splitting, whereby a series of backward-propagating pulses
break from the initially forward-propagating pulse, when an
electric field is applied.2,3 In a two-dimensional configuration
applying an electric field has been observed to cause circularly
propagating waves (target patterns) to break with the free ends
forming into spirals;3-6 then, with the possibility of wave
recombination and further wave breaking, complex dynamics
can result. The effect of electric fields applied to spirals has
been seen to cause both shift and drift of the spiral centers,7-12
to change both the wavelength and the period of spiral waves,13
and to cause the spiral centers to merge into pacemakers for
target patterns.9,14 Most of the features observed in the BZ
experiments have also been reported as arising in models of
these systems.3-10,15-18
Experimental studies into the effects of applying electric fields
to front waves have been concerned mostly with systems based
on the iodate-arsenous acid reaction. The initial studies26
showed that the speed of propagation of the front could be
substantially changed in the electric field, with total wave
annihilation also being possible in fields of sufficient strength.
More recent experimental treatments27 have revealed that
applying electric fields to this system can also alter the local
concentrations sufficiently within the reaction zone to change
the local reaction dynamics and hence the outcome of the overall
reaction.
Here we consider the effects of applying electric fields to
waves propagating in the iodate-arsenous acid system in more
detail. We start by deriving a spatially distributed model for
this system, based on Dushman-Roebuck kinetics.28,29 We
analyze this model in terms of the corresponding traveling wave
equations. Without the electric field the nature of the fronts
propagating in this system and, in particular, the final products
of reaction, depend principally on the stoichiometry factor
[H3AsO3]0
General models for electric field effects on ionic reactions,
based on material balances in a spatially distributed system and
including mass transport by both molecular (Fickian) diffusion
and by electrochemical migration of the ionic components, have
been proposed.19 Reaction mechanisms of different complexities
have beed studied, with perhaps the simplest being reaction
schemes based on a single autocatalytic reaction step.20-25 These
latter schemes, which are essentially models for front waves,
have been analyzed in considerable detail. They have been
shown to exhibit a, perhaps unexpectedly, wide variety of
different responses including wave acceleration and deceleration,
wave splitting, and separation of the reacting species into distinct
S0 )
-
[IO3 ]0
representing the ratio of the initial concentrations of arsenous
acid and iodate.28-30 Without the electric field different reaction
pathways are seen depending on whether S0 > 3 (IO3- is fully
consumed, I2 is an intermediate, some H3AsO3 remains, and I-
is a reaction product), 5/2 < S0 < 3 (both the initial reactants
IO3 and H3AsO3 are fully consumed and I-, I2 are the final
-
-
products), or S0 < 5/2 (H3AsO3 is fully consumed, some IO3
remains, I- is an intermediate, and I2 is a reaction product).
Our analysis of the traveling wave equations with the electric
field effects included shows that the structure of the reaction
front can be characterized in terms of S0 and the parameter ψ
≡ E/V, where E and V are dimensionless versions of the applied
electric field strength and the propagation speed of the wave,
respectively. The front dynamics are seen to have a different
† Department of Chemical Engineering, Prague Institute of Chemical
Technology.
‡ Center for Nonlinear Dynamics of Chemical and Biological Systems,
Prague Institute of Chemical Technology.
§ University of Leeds.
10.1021/jp001157g CCC: $19.00 © 2000 American Chemical Society
Published on Web 09/14/2000

Reaction Fronts in the Iodate-Arsenous Acid System
J. Phys. Chem. A, Vol. 104, No. 40, 2000 9137
structure in different regions of ψ-S0 parameter space, thus
giving the conditions for which the net stoichiometry of the
overall reaction changes. A series of experiments for a range
of values of S0 and electric field intensities is described. These
show clearly the change in the overall outcome of the reaction
that can arise when an electric field is applied. The experimental
results are further analyzed in terms of the ψ-S0 diagram
derived from the model, and reasonably good agreement
between the two is demonstrated.
2. The Model
The oxidation of arsenous acid (AA) by iodate in liquid phase
consists of two coupled reaction steps, each of them consuming
a product of the other reaction. These two reaction steps are
the well-known Dushman-Roebuck scheme (see refs 28 and
29, for example):
IO3- + 5I- + 6H+ f 3I2 + 3H2O;
rate R1 ) (k1 + k2[I-])[I-][IO3 ][H+]2 (1)
-
H3AsO3 + I2 + H2O f H3AsO4 + 2I- + 2H+;
k3[I2][H3AsO3]
rate R2 )
(2)
[I-][H+]
Figure 1. Measured dependence of pH and electric conductivity K on
the stoichiometry factor S0. ∆, initial; *, fully reacted mixtures.
The AA-iodate reaction is autocatalytic in iodide and thus the
reaction cannot proceed until some iodide or iodine (or both)
is present in the reaction mixture. The values of the rate
constants k1, k2, and k3 are given28,29 as k1 ) 4.5 × 103 M-3
a ) a0aj, b ) a0bh, x ) a0xj, y ) a0yj, t ) tRht,
r ) (tRD0)1/2jr (3)
s-1, k2 ) 1.0 × 108 M-4 s-1, k3 ) 3.2 × 10-2 M s-1
.
where r and t are space and time co-ordinates and a, b, x, and
y are the concentrations of A-, B, X-, and Y, respectively. Here
The experiments performed using the AA-iodate system are
often done in a buffered solution (keeping [H+] constant29), or
if this is not the case (as here), the measured pH is found to
remain virtually constant throughout the range of concentrations
employed in the experiments (see also Harrison and Show-
alter31). For our experiments the change in pH measured before
the reaction and in the fully reacted mixture is shown in Figure
1a for the range of stoichiometry factors S0 used. The figure
shows that there is a decrease in the pH of between 5% and
10% during the course of the reaction. This leads us to take
[H+] as constant and to consider a model involving the four
reactant species A- ≡ IO3-, B ≡ H3AsO3, X- ≡ I-, and Y ≡
I2. Our previous studies on traveling waves in autocatalytic
systems20-25 have shown that it was essentially only differences
in the diffusion coefficients of the ionic species that gave rise
to qualitatively different behavior. This leads us to take different
diffusion coefficients D0 and DX for A- and X-, respectively,
and for simplicity, we assume that B and Y have the same
diffusion coefficient D0 as A-. On the assumption that there
are sufficient positive ions (mostly H+) present to maintain local
electroneutrality, we can take the electric field to be a constant,
E . A formal justification for making this approximation from
the general equations for a reacting ionic system derived by
Snita and Marek19 is given by Merkin et al.22
tR is a reaction time based on reaction 1, namely tR
)
(k2a0 [H+]2)-1. We then express the resulting dimensionless
reaction-diffusion-migration equations in terms of the traveling
coordinate ú ) jr - Vht, where V (>0) is the (constant)
dimensionless wave speed. This leads to the traveling wave
equations
2
a′′ + (V + E)a′ - R1 ) 0
b′′ + Vb′ - R2 ) 0
(4)
(5)
Dx′′ + (V + DE)x′ - 5R1 + 2R2 ) 0
y′′ + Vy′ + 3R1 - R2 ) 0
(6)
(7)
on -∞ < ú < ∞ (primes denote differentiation with respect to
ú). In eqs 4-7
FE(D0tR)1/2
E )
(dimensionless electric field) and
RgT
DX
D0
D )
Initially we assume that only A- (IO3-) and B (H3AsO3) are
present in the reactor, uniformly distributed at concentrations
a0 and b0 respectively. A small amount of X- (I-) is then
introduced locally to initiate the reaction. This leads to the
formation of reaction-diffusion waves propagating away from
the initiation site into the unreacted medium. To derive the
equations for these traveling waves, we start by making the basic
equations dimensionless, writing
where F and Rg are Faraday’s and the gas constants and T is
absolute temperature (taken as constant).
κby
x
R1 ) ax(x + µ) and R2 )
are the dimensionless versions of the reaction rates given in (1)

9138 J. Phys. Chem. A, Vol. 104, No. 40, 2000
Forsˇtova´ et al.
and (2), with parameters
(ii) xs * 0, ys * 0 (as ) 0, bs ) 0). For this case eqs 13 and
14 give
k1
k3
µ )
, κ )
2S0 - 5(1 + ψ)
(1 + Dψ)
k2a0 [H+]3
2
k2a0
ys ) 3(1 + ψ) - S0, xs )
requiring that
(17)
The wave is propagating into the unreacted region so that
a f 1, b f S0, x, y, f 0 as ú f ∞
(8)
S
2S
0 - 1 < ψ < 0 - 1
(18)
3
5
where S0 ) b0/a0 is the stoichiometry factor (as given above).
At the rear of the wave the reactions are complete and uniform
concentrations are attained. Thus
We term this the intermediate case (all the AA and iodate
are consumed and both iodide and iodine are final products).
The overall reaction is
a f as, b f bs, x f xs, y f ys as ú f -∞
(9)
S0H3AsO3 +IO3- + (6 - 2S0)H+ f (2S0 - 5)I- + (3 -
S0)I2 + S0H3AsO4 + (3 - S0)H2O
where as, bs, xs, and ys are nonnegative constants to be
determined, and where we must have
as ) 0 or xs ) 0 and bs ) 0 or ys ) 0
(10)
(iii) as * 0, ys * 0 (bs ) 0, xs ) 0). Equations 13 and 14
give for this case
so that R1 ) 0 and R2 ) 0 at the rear of the wave.
A consideration of eqs 4 and 6 shows that we must also have
5(1 + ψ) - 2S0
5(1 + ψ)
S0
as )
,
ys )
(19)
5
V + E > 0 and V + DE > 0
(11)
requiring that
We find that the conditions for the occurrence of the various
possibilities at the rear of the traveling waves inherent in (10)
are most readily expressed in terms of the parameter ψ ) E/V.
Conditions 11 then become
2S
ψ > 0 - 1
(20)
5
This is the iodate-excess case (all the AA is consumed), having
the overall reaction
1
D
ψ > -1 for D e 1 or ψ > - for D > 1 (12)
5H3AsO3 + 2IO3- + 2H+ f I2 + 5H3AsO4 + H2O
We can combine eqs 4-7 in two independent ways so as to
eliminate the reaction terms R1 and R2. If we then integrate the
resulting equations and apply boundary conditions 8 (at the front
of the wave), we obtain
The various cases are illustrated in Figure 2a (for D e 1 )
and Figure 2b (for D > 1). Note that, without the electric field,
ψ ) 0 and the conditions on S0 for the different reaction
pathways to apply given by Merkin and Sevcikova30 are
recovered.
5(a′ + (V + E)a) - 2(b′ + Vb) - (Dx′ + (V + DE)x) ) 5
(V + E) - 2VS0 (13)
There are several points to note about results 16, 18, and 20
showing the possible effect of applying an electric field on
reaction selectivity. First, in terms of our dimensionless model,
these results depend only on the stoichiometry of reactions 1
and 2 and not on the specific details of the reaction kinetics.
However, we note that E and V, though not ψ, are made
dimensionless using tR and hence depend on the reaction kinetics
through this expression. Second, only the diffusion coefficients
of the ionic species A- and X- (through the effect on the
electromigration terms) affect these conditions, having different
diffusion coefficients for the nonionic species B and Y would
not alter them. Third, applying an electric field changes the value
of ψ, which may be either positive or negative depending on
the orientation of the field. Thus we may be able to change ψ
in such a way so as to move from one region of the ψ -S0
parameter plane into another (see Figure 2). This would then
signal a change in the reaction selectivity as now different
reactant species would have nonzero concentration at the rear
of the wave.
3(a′ + (V + E)a) - (b′ + Vb) + (y′ + Vy) ) 3(V + E) - VS0
(14)
We now apply boundary conditions 9 (at the rear of the wave)
in eqs 13 and 14, treating the various cases in (10) in turn. We
start by noting that, if we take both as * 0 and bs * 0, then xs
≡ 0, ys ≡ 0 and there is no wave. This then leaves three other
possibilities.
(i) xs * 0, bs * 0 (as ) 0, ys ) 0). In this case eqs 13 and 14
give
1 + ψ
1 + Dψ
bs ) S0 - 3(1 + ψ), xs )
(15)
where ψ ) E/V as above. The requirement that both bs and xs
be positive then gives the conditions, in terms of S0 and ψ, for
this case to hold, namely that
S
ψ < 0 - 1
(16)
An alternative way to see how changing ψ may affect the
reaction selectivity is to plot ys against S0/(1 + ψ), as shown in
Figure 2c. We can think of S0/(1 + ψ) as a “modified
stoichiometry factor” for the overall reaction induced by the
electric field. By applying an electric field, the value of ψ (either
positive or negative) will be changed (from ψ ) 0 with E ) 0)
and hence the position on the horizontal axis will be moved.
3
(on using conditions 11 and 12). This is the AA-excess case
(all the iodate is consumed) for which the overall reaction reads
3H3AsO3 + IO3- f I- + 3H3AsO4

Reaction Fronts in the Iodate-Arsenous Acid System
J. Phys. Chem. A, Vol. 104, No. 40, 2000 9139
Sevcikova25 suggest that there will be a positive upper bound
on E for traveling waves to form. Thus, for sufficiently strong
fields, wave propagation toward the negative electrode can be
totally suppressed, a feature observed in the previous studies.26
There is no such (theoretical) restriction on the electric field
strength for waves propagating toward the positive electrode,
with ref 25 suggesting that ψ f -1/D as E f -∞. These
conclusions, derived on the assumption that κ is large, apply
strictly only to the case S0 > 3. For S0 < 3 the wave structure
is more complicated,30 though we did find that the wave speed
was not greatly changed from the value calculated assuming
only cubic autocatalytic kinetics for S0 g 2 (at least without
the electric field). Hence, we may expect a similar situation on
E to hold for these lower values of S0 as well.
3. Experiments
3.1. Experimental Procedure. The experiments were per-
formed in a specially designed planar reactor27 of approximate
size 4 × 13 cm in which a thin horizontal layer of the reaction
medium occupies a 4 cm × 4 cm area in the middle of the
reactor. This layer, of depth 0.06 cm, is enclosed between the
bottom of the reactor and a glass cover. Thermostated water
(at 25 °C) circulated through the reactor, ensuring a constant
temperature during the experiments.
A circular reaction front was initiated at the center of the
thin layer by applying a dc voltage (-1 V) on a platinum wire
electrode immersed in the reaction medium through a hole in
the glass cover. After the reaction had been started, the platinum
wire electrode was removed and the reaction front was allowed
to spread through the layer in the form of an expanding circle
until it reached a predetermined distance (0.7 cm) from its
initiation site. A planar dc electric field was then applied to the
reactor through two platinum plate electrodes placed a distance
6.9 cm apart along the sides of the thin layer in the excess
reaction mixture surrounding it. The electric voltage was kept
constant in the course of each experiment, and the electric
current passing through the reaction mixture was registered
every 20 s.
The progress of the reaction was visualized by adding a starch
indicator to form a colored complex with the iodine arising
during the course of the reaction. The experiments were
monitored by a CCD camera and recorded on a VHS com-
mercial videorecorder for further evaluation by image-processing
packages, including a frame grabber. A rectangular window was
placed on the grabbed images (Figure 3, first column) to restrict
the tracing of front propagation to those parts of the front that
propagate parallel to the electric field intensity vector. Time
series images of this rectangular window give space-time plots
in the direction of the field (see Figure 3). From these images
the velocities of front propagation, both with and without an
electric field, and changes in the net reaction stoichiometry could
be determined.
Reaction mixtures with various ratios of initial concentrations
of reactants S0 (given in Table 1) were used to investigate the
effects of an electric field on the net reaction stoichiometry. A
reaction mixture was prepared in a thermostated, well-mixed
reactor into which the volumes of stock solutions were added
in the amount and order as listed in Table 1. Arsenous acid
arose directly in the well-mixed reactor by mixing an appropriate
volume of 0.05 M purchased solution of NaAsO2 with an
equimolar amount of concentrated sulfuric acid. A stock solution
of agar gel was prepared by boiling for a short while 0.125 g
of agar gel in 10 mL of distilled water and then adding another
10 mL of water to it. A 6.4 mL volume of this stock agar gel
Figure 2. Regions in the ψ-S0 parameter plane (ψ ) E/V ) derived
from the model where waves with different nonzero concentrations of
reactant species at their rear (different reaction selectivities) arise for
(a) D e 1 and (b) D > 1. (c) A plot, not to scale, of ys (as given by
expressions 17 and 19) against S0/(1 + ψ). The regions where different
net stoichiometries apply are labeled.
This has the effect of changing the value of ys and, if it is a
sufficiently large change, in moving to another type of net
stoichiometry. This is a useful approach for interpreting the
experimental results as it is ys, the I2 concentration at the rear
of the wave, and, in particular, the color change it produces in
the starch indicator that are used mainly to decide which type
of net stoichiometry has resulted from applying the electric field.
The parameter ψ involves both E, which is known and can
be varied in the experiments, and the wave speed V, which we
expect to depend on E (as well as on the other parameters) with
V being increased for waves traveling toward the positive
electrode and decreased for waves traveling toward the negative
electrode.26,27 Thus a direct calculation of ψ requires the full
solution of the traveling wave equations (4-7) to determine V.
However, we can gain some insight into how V (and hence ψ)
may vary with E from our previous studies.25,30 For the
conditions that pertain in the experiments (described below) the
parameter κ is large, typically taking values between 40 and
130. Under the assumption of large κ,30 the overall reaction
mechanism can be represented to a good approximation by a
cubic autocatalytic rate law, the case treated by Merkin and
Sevcikova in detail.25
Taking the values for the diffusion coefficients32 gives D =
1.9, and in this case (D > 1), the results given by Merkin and

9140 J. Phys. Chem. A, Vol. 104, No. 40, 2000
Forsˇtova´ et al.
Figure 3. The response of various types of propagating front in the oxidation of arsenous acid by iodate to an imposed electric field. The snapshots
in the first column, (a), (f), and (k), show the circular front propagating without an electric field being applied; the size of the monitored area is
approximately 3 × 3 cm. The dark spot at the center marks the initiation site. Space-time plots in the next columns, constructed as a succession
of images from the window, trace the changes in both the position of the two fronts and the products formed behind these fronts during 2 min
(approximately) after the field was switched on. The lightest gray color corresponds to a colorless medium, either unreacted or reacted, containing
no iodine; the darker the color the more iodine is present. 4, ], and O represent AA-excess, intermediate, and iodate-excess net stoichiometries,
respectively.
TABLE 1: Composition of the Reaction Mixtures at Different Values of S0, in Terms of the Volume V (mL) and the
Concentration c (mol/L ) of the Stock Solutions
S0
3.34
2.96
2.77
2.58
2.29
1.91
1.0
compound
H2O
H2SO4
NaAsO2
AgNO3
starch (w/v) %
agar (w/v) %
NaIO3
V
c
V
c
V
c
V
c
V
c
V
c
4.2
0.2
7.0
0.2
1.0
6.4
1.0
5.0
0.2
6.2
0.2
1.0
6.4
1.0
5.4
0.2
5.8
0.2
1.0
6.4
1.0
5.8
0.2
5.4
0.2
1.0
6.4
1.0
6.4
0.2
4.8
0.2
1.0
6.4
1.0
7.2
0.2
4.0
0.2
1.0
6.4
1.0
1.761
0.05
1.563
0.05
1.45
1.360
0.05
1.204
0.05
0.05
0.05
3 × 10-4
3 × 10-4
3 × 10-4
3 × 10-4
3 × 10-4
3 × 10-4
8.0
8.0
8.0
8.0
8.0
8.0
0.625
0.1047
0.625
0.1047
0.625
0.1047
0.625
0.1047
0.625
0.1047
0.625
0.1047
solution was added to the well-mixed reactor after it had cooled
in a water bath to approximately 40 °C. All the reaction mixtures
used consist of 5.235 × 10-3 M NaIO3, 0.4 w/v % starch, 3.0
× 10-6 M AgNO3 (added in order to limit the spontaneous
initiation of the reaction by traces of iodide present in the
purchased NaIO3 ), and 0.2 w/v % agar gel (added in order to
prevent hydrodynamical flows in the layer of the reaction
mixture). Thus, the initial concentration of iodate was kept
constant in all experiments and the ratio of initial concentrations
of reactants was changed by changing the amount of arsenous
acid.
After mixing all the reactants, some of the reaction mixture
was poured into the planar reactor. The rest of the mixture was
used to measure the electric conductivity K and the pH both
before and after the reaction had taken place. Unlike the
experiments performed previously,26,28 no buffer solutions were
added to the reaction mixture and thus the pH decreases slightly
during the reaction (see Figure 1) due to the production of
arsenic acid, which is a stronger acid than arsenous acid (the
pK of H3AsO3 is 9.294 while the pK1 of H3AsO4 is 2.19). The
higher degree of arsenic acid dissociation to ions, as compared
to arsenous acid, leads also to an increase in the electric
conductivity during the course of the reaction. Both pH and K
depend on S0 as can be seen in Figure 1.
3.2. Results and Discussion. 3.2.1. Front Propagation under
Electric Field Free Conditions. For each value of the stoichio-
metric factor S0 chosen several experimental runs were per-
formed in which the propagation of the front throughout the
whole layer (over a distance of 20 mm) was followed under
electric field free conditions. The velocity of front propagation
was found to remain constant over each run (see also Figure 3,
second column). Thus we can exclude the effects of both the
aging of the reaction mixture and the curvature of the growing
circle of the front on the velocity of propagation. The changes
in the propagation velocity observed when an electric field is
applied can then be ascribed fully to the effects that the field
produces.
The dependence of the propagation velocity V on the
stoichiometric factor S0 under electric field free conditions is
shown in Figure 4. The velocity increases with S0 by about 35%
over the range of S0 (S0 ) 1.9 to S0 ) 3.34) used in the
experiments (0.9 mm/min at S0 ) 1.9 to 1.4 mm/min at S0 )

Reaction Fronts in the Iodate-Arsenous Acid System
J. Phys. Chem. A, Vol. 104, No. 40, 2000 9141
In our case, no difference in the velocity of propagation was
observed whether the reaction mixture contained AgNO3 or not.
For S0 > 3 the velocities of front propagation measured by
Hanna et al.28 and in this work are in reasonably good
agreement.
3.2.2. Front Propagation in the Imposed Electric Field. The
changes in the net stoichiometry of the reaction occurring within
reaction fronts in applied electric fields for three representative
values of S0 are shown in Figure 3. The first column in this
figure illustrates the circular reaction fronts which form without
the electric field applied for the AA-excess (S0 > 3), intermedi-
ate (5/2 < S0 < 3), and iodate-excess (S0 < 5/2) cases. Figure
3a shows that iodine is formed only as an intermediate within
the reaction front for the AA-excess case and is not seen in the
reacted mixture behind the wave front (i.e., the region inside
the dark circle). The grayish color behind the thin dark circle
in Figure 3f indicates that more iodine is formed within the
reaction front in the intermediate case and that its concentration
decreases in the region behind the reaction front. The dark disk
seen in Figure 3k for the iodate-excess case implies that a large
amount of iodine is formed within the reaction front. The space-
time plots given in the second column (Figure 3b,g,l) confirm
that the reaction front expands with a constant velocity for each
of these values of S0.
Figure 4. Experimental dependence of the front propagation velocity
on the stoichiometric factor S0 under electric field free conditions.
3.34). A mathematical analysis of a model defined by eqs 4-7,
for electric field free conditions, has been performed by Merkin
and Sevcikova.30 This shows only about a 5% increase in the
dimensionless wave speed V over this range of S0 (see Figure 2
in that paper). The theoretical results are valid only for κ large
and, for the experimental conditions, κ changed from κ ) 128
(at S0 ) 1.9 ) to κ ) 39 (at S0 ) 3.34). The results30 show that
the wave speed V changes only very slightly even over this
relatively large change in κ. However, the dimensional wave
speed V is related to V by
The space-time plots given in the next columns of Figure 3
trace the positions of the reaction fronts after the electric field
was switched on. These illustrate the changes this causes in the
composition of the reacted mixture, visualized by changes in
the color behind the propagating reaction front, as compared to
the zero-field cases shown in the second column. The types of
color change (to clear for the AA-excess case, to dark for the
iodate-excess case, and to something in between for the
intermediate case) observed in the region behind the reaction
front is used to decide the change in the net stoichiometry that
has taken place after the field was applied.
2 1/2
V ) V(D0k2a0 ) [H+]
(21)
Since most of the terms in (21) remain the same for all
experiments, the velocity V depends only on V and [H+], and
since V remains virtually constant over the range of S0 and κ in
the experiments, V depends on [H+] only. At S0 ) 1.9 the
measured pH ) 2.36, giving [H+] ) 0.0044 M, and at S0 )
3.34, pH ) 2.17, giving [H+] ) 0.0067 M. This increase in pH
leads to an increase in the velocity V of about 32% from (21),
in good agreement with the experimentally observed values.
In agreement with the analytical results30 we did not observe
any changes in the propagation velocity during the course of
an experimental run in mixtures with S0 < 3. This is in
contradiction to experimental observations reported by Hanna
et al.28 Their experimental conditions28 are very similar to ours;
the differences account for a 10 times lower concentration of
starch indicator, the absence of agar gel, the presence of a
buffer,28 and the presence of AgNO3 in our experiments. To
exclude the influence of a higher starch concentration, which
could decrease the effective diffusional transport of both iodine
and iodide by bounding large fractions of them, several runs
were performed with S0 ) 2.0 decreasing stepwise the starch
concentration. The front velocity, though increasing with the
decreasing starch concentration, nevertheless stayed constant
over the lifetime of the front in the reactor even for the same
starch concentration as used by Hanna et al.28
We have also performed several experiments with no AgNO3
added, for mixtures with S0 ) 2.0 and 0.04 w/v % starch (the
amount used by Hanna et al.28), to estimate the effects of AgNO3
on the propagation velocity. Normally, when no AgNO3 is
added, traces of I- in the reaction mixture ahead of the front
may cause the reaction to proceed slowly thus making the
medium ahead of the front more susceptible to a burst of
autocatalysis when a front arrives. We thought this may be the
cause of the linearly increasing propagation velocity for S0 <
3.0 reported by Hanna et al.,28 especially because a decreasing
S0 was obtained by increasing the amount of NaIO3 and,
consequently, the amount of trace I- in the reaction mixture.
The first row of space-time plots in Figure 3 (c-e) document
the changes in the overall reaction within the reaction front for
a stoichiometry factor S0 ) 3.34. As no color changes are
observed behind the left-propagating front, we conclude that
the reaction remains of the AA-excess type for the range of
voltages chosen. However, at 5 V we begin to see color changes
behind the right-propagating front, moving toward the negative
electrode. The darkening of the reacted mixture with increasing
voltage indicates an increasing amount of iodine in the reacted
mixture, with the darkness intensity appearing evenly distributed
at 7 V (Figure 3e). At even higher voltages the darkness intensity
is the same as at 7 V, and thus we assess that the overall reaction
within the right-propagating front is of the intermediate type
for voltages 5 and 6 V and becomes iodate-excess type for
voltages 7 V and higher.
The second row of space-time plots in Figure 3 (h-j)
illustrate the change in the overall reaction when an intermediate
type of reaction front (S0 ) 2.77 ) is subjected to an imposed
electric field. Without the field both iodine and iodide are
produced by the reaction, as is manifested by the gray color
behind the reaction zone (Figure 3f,g). When the electric field
is applied, the reacted mixture behind the left-propagating front
becomes colorless at 2 V, indicating that it has changed to AA-
excess type. The darkening of the reacted mixture behind the
right-propagating front with increasing voltage implies that more
iodine is being produced at the expense of iodide and, at 4 V,
the color change indicates that iodate-excess stoichiometry has
been reached.

9142 J. Phys. Chem. A, Vol. 104, No. 40, 2000
Forsˇtova´ et al.
TABLE 2: Calculated Values of the Propagation Velocities
and Electric Field Intensities E(V m-1) for the Experiments
Shown in Figure 4a
R
voltage V- V+
E
E/V- E/V+ I (mA) K (S m-1
)
3.34
3.34
3.34
3.34
2.77
2.77
2.77
2.29
2.29
2.29
2.29
4
5
6
7
1
2
4
6
8
1.25 1.58 (81 455 -306
1.23 1.66 (105 510 -378
1.22 1.76 (125 612 -426
1.20 1.82 (158 792 -522
1
0.54
0.5
0.49
0.5
0.44
0.43
0.42
0.35
0.35
0.34
0.35
1.2
1.4
1.8
0.1
0.4
0.8
1
1.4
1.6
1.9
2.19 2.28 (10
30 -24
2.02 2.30 (41 120 -108
1.94 2.42 (84 258 -210
0.93 1.40 (125 804 -528
0.89 1.53 (175 1182 -684
0.68 1.63 (206 1818 -756
0.46 1.79 (238 3102 -798
9
10
a V+ and V- (mm/min) denote the velocities of the fronts propagating
toward the positive and negative electrode, respectively. Also given
are values of E/V+ and E/V- (×104 V S m-2).
Figure 5. Experimental dependence of the front propagation velocity
on the intensity of the applied electric field E for different values of
the stoichiometric factor S0. Positive (negative) values of E means that
a front propagates toward the negative (positive) electrode. The numbers
represent the values of S0.
Figure 6. Diagram showing the different reaction products observed
behind the reaction fronts propagating toward the positive (E/V < 0)
and negative (E/V > 0) electrodes. The symbols 4, ], and O indicate
the assumed net stoichiometries corresponding to the AA-excess,
intermediate, and iodate-excess cases respectively, as in Figure 4.
The third row of space-time plots in Figure 3 (m-o) shows
the change in the overall reaction caused by applying an electric
field to an iodate-excess type (S0 ) 2.29) reaction front. Without
an electric field the overall reaction produces iodine but no
iodide and so the reacted mixture is dark (Figure 3k,l). Under
the imposed electric field, the first color change is seen at 6 V
(Figure 3m) behind the left-propagating front and we can assess
the overall reaction as then being of the intermediate type. The
color intensity decreases with increasing voltage (Figure 3m-
o) behind the front propagating to the positive electrode, with
the reaction mixture becoming colorless at 9 V (Figure 3o).
Thus we conclude that the transition from intermediate to AA-
excess stoichiometry occurs between 8 and 9 V.
The velocity of propagation of the reaction fronts and the
corresponding electric field intensity E were evaluated for the
various values of S0. The velocities were calculated from the
positions of the reaction fronts taken from the space-time data,
using a least-squares fit. The electric field intensity was
determined from the expression
electric field intensities for the experiments shown in Figure 3
are given in Table 2.
In each experiment, velocities of fronts propagating in the
direction of (toward the negative electrode) and against (toward
the positive electrode) the electric field vector were evaluated
from the space-time plots by tracing the positions of the two
fronts in the window (see Figure 3). Fronts propagating toward
the negative electrode are slowed (or can stop altogether when
field intensity is high enough); fronts propagating toward the
positive electrode are accelerated.
Figure 6 includes all the measured data showing the regions
of different net stoichiometry (reaction selectivity) in the ψexpt
(≡E/V)-S0 plane. We can see from this figure that the individual
regions of different net stoichiometry form well-defined areas
and do not overlap, in agreement with our analysis of the
traveling wave equations. Using (3) we obtain
I
E )
SK
RgT
ψexpt
)
ψ ) 2.4 × 107ψ
(22)
D0F
where I (mA) is the average value of the current passing through
the reaction medium during a given experiment, S is the cross
section as given by the depth of the reaction layer and its width
(S ) 2.28 × 10-5 m2), and K (S m-1) is the conductivity of the
medium calculated as the average of the conductivities of the
initial and reacted mixture measured in the experiment. We
found that the current was stable, changing by less than 5%
during the course of an experimental run. Dependence of the
front propagation velocity (V) on the average field intensity (E)
is shown in Figure 5; values of the propagation velocities and
32
at 25 °C on taking a value for D0 as D0 ) 1.078 × 10-9 m2
s-1. We use (22) to determine the straight lines equivalent to
the lines ψ ) (S0/3) - 1 and ψ ) (2S0/5) - 1 shown in Figure
2, which distinguish between the different types of net stoichi-
ometry. These lines are also plotted in Figure 6.
The general trend of the results shown in Figure 6 is in
agreement with our theoretical predictions. The AA-excess cases
tend to lie below the intermediate cases which, in turn, lie below
the iodate-excess cases, and follow the general pattern shown

Reaction Fronts in the Iodate-Arsenous Acid System
J. Phys. Chem. A, Vol. 104, No. 40, 2000 9143
in Figure 2a,b. There are a few cases where there is a
discrepancy between prediction and experiment. These occur
around the straight lines drawn on the figure to show the
changeover in the net stoichiometry. There are several possible
explanations for this. First, we have used, in (22), a value for
D0 determined for an infinitely diluted binary mixture. This gives
the right order of magnitude, but it could be out by a numerical
factor, slightly altering the slopes of the lines. A second
possibility could arise from errors introduced in the calculation
of the propagation speeds V( and E. These are derived quantities
and cannot be measured directly from the experimental results.
Third, and perhaps much more likely, is the fact that it is
difficult to make a clear distinction between the different types
of net stoichiometry particularly where they change type. There
is a smooth transition in the iodine concentration at the rear of
the wave as the electric field (and hence ψ ) is varied; see Figure
2c. This figure shows that small changes in ψ lead to only small
changes in ys and hence to only small color changes in the starch
indicator, making distinguishing the boundary between types
difficult. However, given these possible sources of error and
that the lines in Figure 6 were drawn using only (22) with no
attempt to fit them to the observed data being made, there is
reasonably good agreement between our theory and experimental
observations.
Acknowledgment. This work was supported by Grant No.
VS96073 from MSMT (Ministry of Education, Czech Republic)
and a travel grant from the Royal Society, London.
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A number of experiments have been performed following the
propagation of reaction fronts in the arsenous acid-iodate
system for a wide range of both the intensity of the applied
electric field E and ratios of initial reactant concentrations S0.
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