Spatiotemporal Dynamics of Mixed Landolt Systems in Open Gel

Jun 11, 2010 - Spatiotemporal Dynamics of Mixed Landolt Systems in Open Gel ... Chemomechanical Oscillations Induced by the Landolt Clock Reaction...
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J. Phys. Chem. A 2010, 114, 7063–7069

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Spatiotemporal Dynamics of Mixed Landolt Systems in Open Gel Reactors: Effect of Diffusive Feed Na´ndor Taka´cs, Judit Horva´th, and Istva´n Szalai* Institute of Chemistry, L. Eo¨tVo¨s UniVersity, P.O. Box 32, H-1518 Budapest 112, Hungary ReceiVed: April 26, 2010; ReVised Manuscript ReceiVed: May 31, 2010

In this report we present an experimental study on the spatiotemporal dynamics of the iodate-sulfite-ferrocyanide and the iodate-sulfite-thiourea systems. Both systems are capable of producing nontrivial reaction-diffusion patterns when they are operated in a one-side-fed open spatial reactor. An important parameter of these types of reactors is the time scale of the diffusive feed, which is determined by the “thickness” of the gel and diffusion coefficients of the chemicals. A conical shape gel is used to study the effect of the thickness gradient on the dynamics. We show that spatiotemporal oscillations stop below a critical thickness. It is demonstrated that the period of the oscillations is determined by the time scale of the inhibitory kinetics and the time scale of the diffusive feed together. In the case of the iodate-sulfite-thiourea system we observed the appearance of a stationary iodine front in the presence of the oscillating pH front. An experimentally supported kinetic explanation is given to account this phenomena. Introduction Patterns arising from the interplay of local self-activation and transport processes are ubiquitous in nature.1,2 Chemical reaction-diffusion systems are often used as a paradigm of these phenomena.3-5 Since the pioneering work of Zaikin and Zhabotinsky on the formation of traveling chemical waves in the Belousov-Zhabotinsky reaction,6 a large variety of chemical patterns have been observed in single aqueous phase systems.5 To produce sustained patterns, the system must be kept far from equilibrium, which can be achieved by using open spatial reactors. A typical open spatial reactor consists of a porous material that is in contact with a continuous-fed stirred tank reactor (CSTR).7 The porous material, which is often a hydrogel, avoids all the fluid motions that would disturb the formation of the reaction-diffusion patterns. Among these reactors one of the most popular is the so-called open one-side-fed reactor (OSFR) configuration, where the gel is in contact with the CSTR only through a single surface. Recently, an effective experimental design method was proposed to produce sustained spatiotemporal and stationary patterns in OSFR’s by coupling selfactivatory and inhibitory reactions and by the control of the effective diffusivity of the activator.8 For practical and theoretical reasons, one of the key points of the method is to find appropriate conditions for the development of spatiotemporal oscillations, waves. In this endeavor the importance of the effectiveness of an inhibitory reaction and the kinetic time scale separation, that is, τact , τinh, has been clearly demonstrated.9,10 The time scale of the diffusive feed, τf ) R2/Di, which can be defined as the residence time in the core of the gel, plays also an important role in the development of the spatiotemporal patterns.11-13 Here R is the distance between the CSTR/gel surface and the core of the gel, often called “thickness” and Di is the diffusion coefficient of the actual chemical species i. The feeding time scales of the small ions or molecules do not differ significantly, since their diffusion coefficients are similar. * To whom correspondence [email protected].

should

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However, τf of protons and hydroxide ions are much shorter due to their fast diffusivity. Among the different aqueous phase nonlinear reactiondiffusion systems, the proton autocatalytic reactions are preferably used due to their advantageous properties: (i) the apparent diffusivity of the activator can be nicely controlled by using polyelectrolytes;8-10 (ii) the large variation of the proton concentration during the autocatalytic reaction allows these systems to drive other physicochemical processes, e.g., to shift back and forth equilibrium reactions,14 to induce the mechanical motion of chemoresponsive materials, hydrogels, or DNA filaments;15,16 (iii) the pattern formation can be visualized relatively easily by pH indicators. The prototype of the proton autocatalytic reactions is the Landolt (IS) reaction,17 that is, the oxidation of sulfite ions by iodate ions. It is often used as a classroom demonstration of autocatalysis. The IS reaction is autocatalytic for both protons and iodide ions. However, Ra´bai and co-workers18 pointed out that the dominant positive feedback process is the autocatalytic oxidation of hydrogen sulfite:

IO3- + 3HSO3- f I- + 3SO42- + 3H+

(R1)

The iodide autocatalytic process becomes important only at the end of the oxidation of sulfite when the pH drops below 5:

IO3- + 5I- + 6H+ f 3I2 + 3H2O

(R2)

I2 + HSO3- + H2O f 2I- + SO42- + 3H+

(R3)

During the course of the IS reaction operated in a batch reactor, after a well-defined induction time (often called Landolt time, τi), the pH of the reacting mixture abruptly drops. In a CSTR, bistability between two stationary states can be obtained.19 One of the states is characterized by the low extent of reaction; the pH of the CSTR content is around 8-9. This state we call flow or the “F” state of the CSTR. At the other stationary

10.1021/jp1037624  2010 American Chemical Society Published on Web 06/11/2010

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state, the CSTR content is acidic (pH ∼ 4) and the composition is close to that one would obtain at the thermodynamic equilibrium in a closed systems. We call it the thermodynamic or “T” state of the CSTR. The stability range of these states overlaps over a finite domain of the control parameters (e.g., residence time of the CSTR), which is bistability. In open reactors temporal oscillations can be observed by coupling an appropriate inhibitory reaction with a self-activatory one, where the time scale of the activatory process is shorter than that of the inhibitory one, that is, τact , τinh.5 In the case of the IS reaction, the iodate-ferrocyanide or the iodate-thiourea reactions are capable of playing this role.19-21 Both are proton consuming reactions with similar overall stoichiometries but with different kinetics.

IO3- + 6H+ + 6[Fe(CN)6]4- f I- + 6[Fe(CN)6]3- + 3H2O (R4)

IO3- + 6H+ + 6SC(NH2)2 f I- +

Figure 1. Sketch of the OSFR used with conical shape gel. 2+

3NH3(NH)CSSC(NH)NH3

+ 3H2O (R5)

The stoichiometry of the iodate-thiourea reaction given in (R5) is valid only if the further oxidation of the dithiobis(formamidine) can be neglected and this species is in a double protonated form. The second condition is fulfilled if the pH is below 4.5. These two mixed Landolt systems, the iodate-sulfiteferrocyanide (FIS) and the iodate-sulfite-thiourea (TuIS), are found to be capable of producing nontrivial reaction-diffusion patterns when they are operated in OSFRs.8-10,22-24 Both systems produce spatial bistability, where two stable states with different spatial concentration distributions, not breaking the boundary symmetries, coexist at the same range of parameters. They are capable of showing spatiotemporal oscillation waves above a critical input feed concentration of ferrocyanide and thiourea, respectively. It means that the rate of the inhibitory reaction must exceed a minimum value. However, according to the similarity in the stoichiometries of reactions R4 and R5, one would expect similar wave dynamics. This is not the case. In the FIS reaction the wave dynamics is driven by interactions of counter propagating Bloch fronts.25 On the contrary, in the TuIS reaction a typical relaxation oscillation can be observed.10 A clear difference appears when the effective diffusivity of the protons is reduced by the addition of a large molecular weight anionic polyelectrolyte (e.g., sodium polyacrylate). Above a critical concentration of the polyelectrolyte, both systems produce stationary patterns. They appear as labyrinthine patterns resulting from front instabilities and repulsive interactions in the case of the FIS reaction,25 and as Turing patterns resulting from a Turing symmetry breaking instability in the case of the TuIS reaction.8,10 Here, we present a comparative study on the wave dynamics of the FIS and TuIS reactions, focusing on the effect of feeding time scale. Experimental Section The chemicals, KIO3 (98%, Sigma-Aldrich), Na2SO3 (98%, Sigma-Aldrich), SC(NH2)2 (98.5%, Riedel-de Hae¨n), K4[Fe(CN)6] · 3H2O (99%, Sigma-Aldrich), Bromocresol-green (indicator grade, Sigma-Aldrich), H2SO4 (1 mol/dm3, Fluka),

and agarose (Type I, Sigma-Aldrich) were used without further purification. All the solutions were prepared with deionized water. The batch experiments were made in a thermostated closed vessel (V ) 25 cm3, T ) 30 ( 0.5 °C). The reactions were followed by a pH-electrode (Hanna HII1330B); the data were recorded and digitalized by Consort pH-meter (C861). The CSTR and OSFR experiments were performed in the same reactor. The volume of the reactor was V ) 45 cm3 and it was thermostated to T ) 30 ( 0.5 °C. A peristaltic pump (Gilson Miniplus 2) was used to maintain the input flow. The residence time of the CSTR was τ ) 250 s. The chemical solutions were stored in three separated reservoirs: (1) KIO3; (2) Na2SO3, bromocresol green, K4[Fe(CN)6] or SC(NH2)2; (3) sulfuric acid. The pH indicator switches from blue to light yellow in the 5.4-3.8 pH range. The feed concentration of potassium iodate [KIO3]0, sodium sulfite [Na2SO3]0, and the indicator were fixed at 75, 89, and 0.033 g/dm3, respectively. Here [ ]0 denotes the concentration that the input species would have in the reactor after mixing and prior to any reaction. The feed concentrations of the other species were changed during the experiments and are indicated where appropriate. The state of the CSTR content was followed by a pH electrode. The conical and cylindrical shape OSFR’s are used in this report. The sketch of the reactor is shown in Figure 1. The gels were made of 4% agarose. The typical height of the cones is l ) 40 mm, with a base radius of Rbase ) 2.25 mm. The length of the gel cylinders is around 35 mm, the radius varied between 0.155 and 0.110 cm. They were glued to a holder and immersed in the content of the CSTR. Patterns were observed by transparency and were monitored by a digital fire wire video camera (Imagingsource DFK31BF03). The observations provide information on light transmission patterns across the gel. Experimental Results Batch and CSTR Dynamics. First, we recall the important features of the batch and CSTR dynamics of the FIS and TuIS reactions. In all the experiments presented in this paper, iodate is in large stoichiometric excess over the sulfite if we consider only reaction R1. Complete reduction of iodate to iodide requires an iodate/sulfite ratio of 1/3 or lower. Here, this ratio is around

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SC(NH2)2 + HOSC(NH)NH2 f NH2(NH)CSSC(NH)NH2 + H2O (R8) NH2(NH)CSSC(NH)NH2 + H+ h NH2(NH)CSSC(NH)NH3+

(R9)

NH2(NH)CSSC(NH)NH3+ + H+ h NH3(NH)CSSC(NH)NH32+

Figure 2. pH vs time curves observed in the FIS (a), IS (b), and TuIS (c) reactions. The initial concentrations are26 [KIO3]i ) 75 mmol/dm3, [Na2SO3]i ) 89 mmol/dm3, [H2SO4]i ) 5.4 mmol/dm3, and [K4Fe(CN)6]i ) 20 mmol/dm3 (a), [SC(NH2)2]i ) 5 mmol/dm3 (c).

5/6, which means the end product of the reduction is not only iodide; the reaction of iodate and iodide (R2) must be considered. To study the autocatalytic iodate-sulfite (IS) reaction, we set the initial pH of the reacting mixture of iodate and sulfite to pH ∼ 8 (Figure 2b), at which the initial concentration of HSO3is around 10 mmol/dm3. According to reaction R1 the amount of protons produced in the autocatalytic reaction must equal the amount of the initial HSO3-. After an induction period, around 150 s, the pH of the solution jumps down to ∼3.5. This corresponds to a maximum concentration of protons of 0.3 mmol/dm3, only 3% of the expected value. Then the pH starts to increase to pH 6 within 600 s, due to the proton consuming reaction R2. In the presence of ferrocyanide (Figure 2a) the induction time is slightly shorter while the end pH is higher (∼6.4). The observed shape of the pH vs time curve in the FIS system is similar to that in the IS reaction. The proton consuming process is reaction R2 coupled with the iodine-ferrocyanide reaction R6:

I2 + 2[Fe(CN)6]4- f 2I- + 2[Fe(CN)6]3-

(R10)

The equilibrium constants of reactions R9 and R10 are K9 ) 4.57 × 107 and K10 ) 3.1 × 105, so dithiobis(formamidine) can effectively buffer the system.27 We also checked the direct oxidation of ferrocyanide and thiourea by iodate. The observed pH vs time curves differ from each other in many aspects (Figure 3). First of all, after adding the same amount of sulfuric acid, the initial pH of the solutions are not the same. It is higher in the case of the iodate-ferrocyanide mixture (Figure 3a,b) than in the iodate-thiourea mixtures (Figure 3c,d), due to the buffering effect of ferrocyanide (R11):18

[Fe(CN)6]4- + H+ h H[Fe(CN)6]3-

(R11)

The equilibrium constant of reaction R11 is K11 ) 1 × 103. In the iodate-ferrocyanide reaction the pH of the reacting mixture increases monotonously (Figure 3a,b). The reaction becomes slower as the initial pH increases. During the iodate-thiourea reaction, the pH of the mixture goes through a maximum, and the shape of the pH vs time curve strongly depends on the initial pH of the solution (Figure 3c,d). The sudden increase of the pH at the beginning can be attributed to the fast equilibrium formation of an adduct (R12):28

IO3- + H+ + SC(NH2)2 h HIO3SC(NH2)2

(R12) The following decrease of the pH is the result of an iodide autocatalytic reaction in which reaction R2 is coupled with the multistep oxidation of thiourea to sulfate (R13).20

(R6)

The pH vs time curve of the TuIS reaction (Figure 2c) significantly differs from that of IS or FIS reactions (Figure 2b). The induction time is slightly longer and, after the pH minimum is reached, a sudden jump can be observed up to pH ) 4.5, which is followed by a slow further increase until pH ) 5. This sharp increase of the pH is the result of reactions R7 and R2 together, where the rate of the iodine-thiourea reaction R7 is at least 5 times faster than the analogous iodine-ferrocyanide reaction R6.20

I2 + 2SC(NH2)2 + H2O f 2I- + HOSC(NH)NH2 + 2H+ (R7) The lower end pH of the TuIS reaction, compared to that for the IS reaction, can be understood by considering reaction R8, the buffering effect of dithiobis(formamidine) (R9, R10):21

4I2 + SC(NH2)2 + 5H2O f 8I- + OC(NH2)2 + SO42- + 10H+ (R13) The induction time of this autocatalytic process lengthens as the initial pH of the mixture increases, and it becomes longer than 1000 s when the initial pH is above 3 (Figure 3c,d). At the end of the reaction, the mixture contains visible amount of iodine. In the CSTR and the OSFR experiments we use the input feed concentration of the sulfuric acid ([H2SO4]0) as a control parameter. Increasing [H2SO4]0 increases the [HSO3-]0/[SO32-]0 ratio since the sum of [HSO3-]0 and [SO32-]0 is fixed. At the [KIO3]0/[Na2SO3]0 ) 5/6 ratio used here the induction time of the IS reaction is approximately inversely proportional to the concentrations of iodate and hydrogen sulfite ions: 1/τi ∝ [IO3-]0[HSO3-]0.29 That means an increase of [H2SO4]0 leads to a decrease of τi. The IS reaction, operated in a CSTR under the conditions used here, shows bistability between an alkaline F state (pH ∼

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Figure 3. pH vs time curves observed in the iodate-ferrocyanide (a, b) and iodate-thiourea (c, d) reactions at two different initial sulfuric acid concentrations. The initial concentrations are26 [KIO3]i ) 75 mmol/ dm3, [H2SO4]i ) 0.54 mmol/dm3 (a, c), [H2SO4]i ) 2.7 mmol/dm3 (b, d), [K4Fe(CN)6]i ) 20 mmol/dm3 (a, b), and [SC(NH2)2]i ) 5 mmol/ dm3 (c, d).

8) and an acidic T state (pH ∼ 4). As [H2SO4]0 is increased from zero, the CSTR contents is in the F state up to [H2SO4]0 ) 3.0 mmol/dm3. A further increase of [H2SO4]0 leads to a sudden jump to the T state at which the concentration of iodine is high in the CSTR. Now, by decreasing [H2SO4]0, the T state is stable until [H2SO4]0 ) 0.5 mmol/dm3. Between [H2SO4]0 ) 0.5 and 3.0 mmol/dm3, the system has two stable stationary states. In the extended FIS and TuIS systems we used two different ferrocyanide and thiourea concentrations. When the input feed concentration of ferrocyanide is [Fe(CN)64-]0 ) 10 mmol/dm3, the FIS system is bistable (Figure 4a). The pH values of the stationary states are close to those in the IS reaction, but the range of bistability ([H2SO4]0 ) 3.0-4.5 mmol/dm3) is shifted and smaller. At [Fe(CN)64-]0 ) 20 mmol/dm3 monostable stationary states and large amplitude pH oscillations can be observed (Figure 4b). The maximum pH attained during the oscillations is around pH ∼ 7 while the minimum is about 3.5-4. The typical period of the oscillations is around 7-10 min, which is significantly longer than the residence time of the CSTR (τ ) 4.17 min). The TuIS reaction in a CSTR at [SC(NH)2]0 ) 3 and 5 mmol/ dm3 shows bistability between two steady states (Figure 5). The pH values in these states do not differ significantly from those in the FIS system at [Fe(CN)64-]0 ) 10 mmol/dm3. To obtain temporal oscillations in the CSTR, higher input feed concentrations of thiourea are needed. Since the pH of the stationary T branch is around 4, and the residence time of the CSTR is 250 s, the effect of the autocatalytic overall oxidation of thiourea (R13) is probably negligible. Experiments in Conical OSFR. In all the OSFR experiments, we kept the CSTR content on the alkaline, F stationary state, which means the extent of reaction is almost zero in the CSTR and the gel is fed by a fresh reactant composition. When the IS reaction is operated in a conical OSFR, from zero up to [H2SO4]0 ) 1.5 mmol/dm3 the chemical composition in the gel does not differ significantly from that in the CSTR. We call it the F state of the gel. At [H2SO4]0 ) 1.5 mmol/dm3, a stationary acidic front appears at the base of the cone, where the radius is the largest (Figure 6a). It is visible on the pictures that the outer skin of the cone remains alkaline (light gray color), while the central part is acidic (black color). We call it the M state of the gel. The M state appears when the induction time

Figure 4. CSTR dynamics of the FIS reaction: bistability at [K4Fe(CN)6]0 )10 mmol/dm3 (a) and oscillations at [K4Fe(CN)6]0 ) 20 mmol/dm3 (b). The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/dm3.

Figure 5. CSTR dynamics of the TuIS reaction: bistability at [SC(NH2)2]0 ) 3 mmol/dm3. The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/dm3.

τi of the IS reaction becomes shorter than the feeding time scale τf of iodate and hydrogen sulfite at a given radius. In a conical gel τf decreases continuously from the base to the tip. As [H2SO4]0 is further increased, the M state moves closer to the tip (Figure 6b,c) and finds stationary positions at a smaller radius. We observed stationary fronts at any radius. Spatiotem-

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Figure 6. Stationary M states in a conical gel with the IS reaction at various [H2SO4]0. The input feed concentrations of sulfuric acid are [H2SO4]0 ) 1.5 mmol/dm3 (a), [H2SO4]0 ) 2.0 mmol/dm3 (b), and [H2SO4]0 ) 2.5 mmol/dm3 (c). The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/dm3. Figure 8. Period of the spatiotemporal oscillations as a function of Rosc2 in a conical gel in the FIS reaction at [K4Fe(CN)6]0 ) 10 mmol/ dm3 (a) and [K4Fe(CN)6]0 ) 20 mmol/dm3 (b). The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/ dm3.

Figure 7. Spatiotemporal oscillations in a conical gel in the FIS reaction (a) and a time-space plot made along the center of the cone (b). The input feed concentrations are: [K4Fe(CN)6]0 ) 20 mmol/dm3 and [H2SO4]0 ) 2.8 mmol/dm3. The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/dm3.

poral oscillations cannot develop in the IS system at the conditions used here.13 In the case of the FIS reaction, at both [Fe(CN)64-]0 ) 10 and 20 mmol/dm3, the front of the M state becomes unstable and spatiotemporal oscillations can be observed (Figure 7a). During the oscillations, the low limit of the M state moves back and forth between two critical radii, Rosc and Rmin. A time-space plot of the oscillations, made along the center line of the cone, is shown in Figure 7b. As the M state appears at the base (Rbase ) 2.25 mm) of the cone, it starts to oscillate. As [H2SO4]0 is further increased, the M state moves closer to the tip and oscillates between smaller Rosc and Rmin. The oscillations stop at a lower critical radius. The value of the lower critical radius decreases as [Fe(CN)64-]0 increases. Figure 8 shows the period (Tper) of the spatiotemporal oscillations as a function of Rosc2. The period is longer at [Fe(CN)64-]0 ) 10 mmol/dm3 than at 20 mmol/dm3, which shows the effect of the inhibitory time scale τinh. The spatial amplitude of the oscillations of the M state tip, A ) (Rosc - Rmin)/tan(R) decreases as Rosc decreases. In the TuIS system, at [SC(NH2)2]0 ) 3 and 5 mmol/dm3, spatiotemporal oscillations are also observed. The typical shape of the tip of the acidic front between the M and F states differs from that with the FIS system. During the oscillations, when the front reaches Rmin, a thinner acidic zone (Figure 9) can be seen behind the tip. As the M state appears at the base of the cone, it starts to oscillate. As [H2SO4]0 is increased, the M state moves closer to the tip but still oscillates. The oscillations stop at a lower critical radius. The value of the lower critical radius decreases as [SC(NH2)2]0 increases. Figure 10 shows the period of the spatiotemporal oscillations as a function of Rosc2. The period goes through a maximum, especially at [SC(NH2)2]0 ) 3 mmol/dm3 where the period is about a factor of 2 longer than

Figure 9. Spatiotemporal oscillations in a conical gel in the TuIS reaction (a) and a time-space plot made at the center of the cone (b). The input feed concentrations are [SC(NH2)2]0 ) 3 mmol/dm3, [H2SO4]0 ) 3.2 mmol/dm3, [KIO3]0 ) 75 mmol/dm3, and [Na2SO3]0 ) 89 mmol/ dm3.

Figure 10. Period of the spatiotemporal oscillations as a function of Rosc2 in a conical gel in the TuIS reaction at [SC(NH2)2]0 ) 3 mmol/ dm3 (a) and [SC(NH2)2]0 ) 5 mmol/dm3 (b). The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/ dm3.

that at [SC(NH2)2]0 ) 5 mmol/dm3. Similarly to the FIS systems, the spatial amplitude decreases as Rosc decreases. In the TuIS reaction, a second front appears behind the acid front that connects the M and the F states. According to its dark color we assume that it is an iodine front. As it is presented in Figure 11, this iodine front does not oscillate while the acidic

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Figure 11. Stationary iodine and oscillating pH front in a conical gel in the TuIS reaction (a) and a time-space plot made along the center of the cone (b). The input feed concentrations are [SC(NH2)2]0 ) 5 mmol/dm3, [H2SO4]0 ) 3.2 mmol/dm3, [KIO3]0 ) 75 mmol/dm3, and [Na2SO3]0 ) 89 mmol/dm3.

front does. As [H2SO4]0 is increased, the distance between the acid and the iodine front decreases, and the two fronts merge around the critical radius at which the oscillations of the pH front stop. The appearance of the iodine front seems to be favored at higher input concentration of thiourea. Discussion Our results clearly show that the spatiotemporal dynamics of the FIS and TuIS reactions in OSFR’s are strongly dependent on the feeding time scale of the spatial reactor. The IS reaction, as the core of the present two oscillatory systems, exhibits quite peculiar behavior when operated in an OSFR. It can exhibit oscillatory instability in such a spatial reactor even though no oscillations can be observed in a CSTR.11,13 These OSFR oscillations are probably due to the much faster diffusivity of the protons compared to that of the iodate and hydrogen sulfite. The period of the spatiotemporal oscillations of the IS reaction depends linearly on R2, which supports this explanation. In a stoichiometric excess of iodate, reaction R2 acts as a local proton sink, which may quench the diffusion driven instability. Now, in stoichiometric excess of iodate another source of instability is needed to produce spatiotemporal oscillations. This is a kinetic instability induced by an inhibitory reaction in the systems studied here. The spatiotemporal dynamics is driven by the interplay of the self-activatory and the inhibitory reactions, but the effect of the feeding time scale cannot be neglected either. The input feed concentration of the inhibitory species (ferrocyanide or thiourea) necessary to induce spatiotemporal oscillations depends on the thickness of the gel (R). As the inhibitory reaction is enforced, the period of the oscillations shortens. It means that spatiotemporal oscillations need a balance between the time scales of the local inhibition and the diffusional feed. The properties of the spatiotemporal oscillations observed in the FIS and the TuIS systems are different. We performed additional experiments in a cylindrical OSFR to compare the spatiotemporal dynamics at constant radius. Below a critical [H2SO4]0 the whole gel is in the alkaline F state. In the case of the FIS reaction, at a critical [H2SO4]0 the M state appears at the upper part of the cylinder, and it expands nearly completely in the gel (Figure 12a). The up and down moving fronts change their sign when they reach the ends of the gel. After that, two sharp backward propagating fronts can be seen. The time-space plot in Figure 12a shows clearly these two counterpropagating fronts. In the case of the TuIS reaction, as the M state appears at a critical [H2SO4]0 it expands in the gel. Then, the M state disappears without the formation of clear backfronts. As shown

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Figure 12. Time-space plot of the oscillations in a cylindrical gel with the FIS (a) and TuIS reactions (b). The input feed concentrations are [K4Fe (CN)6]0 ) 10 mmol/dm3, [H2SO4]0 ) 2.2 mmol/dm3 (a) and [SC(NH2)2]0 ) 3 mmol/dm3, [H2SO4]0 ) 2.6 mmol/dm3 (b). The other input concentrations are [KIO3]0 ) 75 mmol/dm3 and [Na2SO3]0 ) 89 mmol/dm3.

on the time-space plot in Figure 12b, a smooth recovery is observed behind the pH front. As we presented, the batch kinetics of the two reactions also differs. In the case of the FIS reaction, the end pH of the reacting mixture is significantly higher than that in the TuIS system. Ferrocyanide consumes protons slower but more efficiently than the thiourea. Furthermore, the iodate-thiourea reaction is much more complex than the iodateate-ferrocyanide one. Importantly, one intermediate product of the oxidation of thiourea, dithiobis(formamidine), acts as a buffer that avoids the further increase of the pH. Figures 8 and 10 clearly show that the period of the spatiotemporal oscillations in these systems is not a linear function of Rosc2 and it depends on the concentration of the inhibitor. It means that the kinetic time scale of the inhibition contributes to the period significantly. At Rosc ) 1 mm T is 17 min (at [Fe(CN)64-]0 ) 20 mmol/dm3) and 5 or 12 min in the TuIS system (respectively at [SC(NH2)2]0 ) 3 and 5 mmol/ dm3). The time scale of the diffusive feed in a 1 mm gel is τf ) 8-16 min if the diffusion coefficient is around (1-2) × 10-5 cm2/s, which means Tper ≈ τf. We assume that the diffusion coefficients in the agarose gel are similar to those in water. However, at larger size, e.g., at Rosc ) 1.5 mm, the observed periods are even shorter than the feeding time scale. The largest difference can be observed in the TuIS systems at [Tu]0 ) 5 mmol/dm3 where Tper ) 6 min compared to the calculated τf ) 19-36 min. That probably resulted from the more complex kinetics of the iodate-thiourea reaction. Similar effects can be observed in a CSTR if we compare the period of the temporal oscillations and the residence time. In the case of the FIS reaction, the period is around 7-10 min at [Fe(CN)64-]0 ) 20 mmol/dm3, longer than the residence time of the reactor (τ ) 4.17 min). In the TuIS reaction at [SC(NH2)2]0 ) 10 mmol/dm3, the period of the temporal oscillations varies between 3.5 and 15 min. The fact that the period can be shorter than the residence time shows again the more complex kinetics of the TuIS system. This kinetic complexity results in the appearance of the iodine front in the TuIS system behind the acidic front. The formation of the iodine front can be accounted for by the combination of reactions R13 and R2. In the CSTR the residence time is too short compared to the induction time of the autocatalysis through (R13) and (R2). However, in the gel the feeding time scale can be much longer (τf . 1000s if R > 1 mm); thus an iodine front

Mixed Landolt Systems in Open Gel Reactors can develop. This stationary front connects a low pH, low iodine and a low pH, high iodine state. Figure 11 at a given [H2SO4]0 shows the pH front oscillates while the iodine front stays at higher radius R. The extent of reaction is quite different at the two positions. The oscillations of the pH front require proton consumption by the partial oxidation of thiourea, as presented in reaction R5. At larger radius, the feeding time scale is longer and makes possible the complete oxidation of thiourea (R13). However, during the complete oxidation, protons are produced and not consumed. The inhibitory reaction disappears in the core. Now when [H2SO4]0 is increased, the distance between the iodine and the acidic fronts decreases. When the two fronts collide, there is no more possibility for oscillations, since thiourea does not consume protons any more. A seemingly similar phenomenon, separated iodine and pH fronts, is observed in the iodate-sulfite-thiosulfate reaction under batch conditions.30 Acknowledgment. We thank Patrick De Kepper for fruitful discussions. We acknowledge the support from the Hungarian Research Fund (77986, 67701), the Bolyai Fellowship, and the Hungarian Development Bank. References and Notes (1) Murray, J. D. Mathematical Biology; Springer: Berlin, 2004. (2) Meinhardt, H. Models of Biological Pattern Formation; Academic Press: London, 1982. (3) Field, R. J., Burger, M., Eds. Oscillations and TraVeling WaVes in Chemical Systems; Wiley: New York, 1985. (4) Kapral, R., Showalter, K., Eds. Chemical Patterns and WaVes; Kluwer Academic Publisher: Amsterdam, 1995. (5) Epstein, I. R.; Pojman, J. An Introduction to Nonlinear Chemical Dynamics; Oxford University Press: New York, 1998. (6) Zaikin, A. N.; Zhabotinsky, A. M. Nature 1970, 225, 535.

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