Monitoring of Spatiotemporal Patterns in the Oscillatory Chemical

J. Phys. Chem. A 2010, 114, 7903–7911

7903

Monitoring of Spatiotemporal Patterns in the Oscillatory Chemical Reactions with the Infrared Camera: Experiments and Model Interpretation Katarzyna Pekala,† Albin Wisńiewski,† Rafał Jurczakowski,† Tomasz Wisńiewski,‡ Małgorzata Wojdyga,† and Marek Orlik*,† UniVersity of Warsaw, Faculty of Chemistry, ul. Pasteura 1, 02-093 Warsaw, Poland, and Warsaw UniVersity of Technology, Institute of Heat Engineering, ul. Nowowiejska 21/25, 00-665 Warsaw, Poland ReceiVed: May 11, 2010; ReVised Manuscript ReceiVed: June 23, 2010

An infrared camera was used for the first time to monitor the progress of traveling fronts in oscillatory chemical reactions, taking the Belousov-Zhabotinsky (BZ) reaction as the test system. The experiments involved comparative visual imaging and infrared thermography measurements for the thin-layer of the BZ solution in the Petri dish, including both aqueous and gel media, the latter one hindering the convection. Infrared thermography experiments that supply information on the temperature distribution at the solution surface were compared with the bulk temperature variations of the stirred solution with BZ reaction, measured simultaneously with the oscillatory variations of the Pt electrode potential. The experimentally observed correlation between the ferroin catalyst concentration and the temperature distribution was compared with the results of numerical modeling of these distributions in 2-D reactor space, based on the classical Oregonator. Analogous experiments were performed for the oscillatory oxidation of thiocyanates with hydrogen peroxide, catalyzed with Cu2+ ions, in search of factors causing the development of traveling fronts, previously reported. The inhomogeneous distribution of the free surface temperature that could contribute to surface instabilities was found. Also, periodical increase and decrease in temperature of solution surface was reported. This was interpreted as periodically predominating cooling of the surface in contact with the surroundings because for the bulk, thermally isolated stirred solution, the temperature monotonically increases. In terms of our ninevariable kinetic model of this system, it was possible to identify the reaction steps responsible for the experimentally observed temperature dynamics and ascribe the appropriate heat effects to them. Our results constitute the first contribution to the thermochemical characteristics of the H2O2-SCN--OH--Cu2+ oscillator. 1. Introduction From the thermodynamic point of view, chemical reactions exhibiting oscillatory behavior are as a rule exothermic, and from the kinetic point of view, they are usually multistep processes (involving feedback loops), each of them having its own contribution to the overall reaction enthalpy. Despite numerous studies of the oscillatory reactions, relatively little attention was paid to their thermochemical characteristics. Even for the Belousov-Zhabotinsky (BZ) reaction, undoubtedly the most intensively studied homogeneous oscillatory process, its thermochemical characteristics are rather rare in the literature. However, temperature gradient can be one of the factors contributing to the formation of spatial or spatiotemporal patterns for the oscillating process running in an unstirred medium. Such gradients can induce spatial distribution of the rate and equilibrium constants as well as the gradients of the surface tension and of solution density, the latter ones being possible sources of the convection, named the Beńard-Marangoni and Beńard-Rayleigh instabilities, respectively. In ref 1, it was indicated that the density-driven convection may also interplay with the isothermal volume changes, caused by differences in partial molar volumes of the oxidized and reduced forms of the metal catalyst, and in this way lead to the so-called multicomponent convection. In turn, Bo¨ckmann et al.2 have * To whom correspondence should be addressed. E-mail: morlik@ chem.uw.edu.pl. Fax: +48 22 822 59 96. Tel: +48 22 822 02 11, ext. 245. † University of Warsaw. ‡ Warsaw University of Technology.

concluded that local temperature inhomogeneities in the BZ reaction are too small to become a source of density-driven convection, which thus appeared to be caused by local concentration changes alone. Concerning the BZ reaction, if it is performed in the ideally stirred reactor with the diathermal walls, the solution temperature (T) increases as a function of time (t) in a staircase manner. The periodically varying slope dT/dt indicates the temporal predominance of reaction steps of different enthalpies and varying reaction rates. Ko¨ro¨s et al. have reported,3,4 that the steepest increase in temperature occurred when the concentration of the oxidized form of the cerium catalyst was decreasing, as simultaneous measurements of the Pt electrode potential revealed. This decrease in [Ce(IV)] was associated with the oxidation of organic species being presumably the most exothermic step, ∆H ) -535 kJ/mol for the oxidation of malonic acid and -711 kJ/mol for bromomalonic acid. In terms of the classical FKN or the Oregonator models, involving three reaction groups (A, B, C), this means that this predominating heat effect can be ascribed to step C, in which the Ce(IV) or Fe(phen)33+ species oxidizes the organic compounds with liberation of Br- ions. In turn, process B, in which Ce(IV) is a product, was found to exhibit a relatively small heat effect (+26.6, -21.7, and +40.7 kJ/mol for Ce(III), Mn(II), and Fe(phen)32+ catalyst, respectively).4 Calorimetric studies of the BZ reaction, leading to similar results, were also carried out by Lamprecht and Schaarschmidt.5 The difference in heat effects of particular reaction steps must turn into temperature gradients

10.1021/jp104299a  2010 American Chemical Society Published on Web 07/12/2010

7904

J. Phys. Chem. A, Vol. 114, No. 30, 2010

in spatiotemporal patterns. For the traveling waves in the excitable BZ medium, Nagy-Ungvarai et al.6 have measured the ca. 1 mM changes of the concentration of cerium ions within the reaction front, which should correspond to the temperature difference of 0.1 K.1 Similar changes for the concentration of ferroin as a catalyst were reported by Wood and Ross.7 Early studies of such local temperature gradients required direct contact of the solution with appropriate sensors that could, however, slightly disturb the local temperature. Therefore, we used more modern equipment, a highly sensitive infrared camera, as the noninvasive tool to visualize the surface temperature distribution, associated with the oscillatory process occurring in the thin layer of the solution. Our aim was to check whether the temperature gradients are detectable for the traveling fronts in the BZ reaction, treated as the test process, and then to detect eventual temperature gradients during the oscillatory oxidation of SCN- ions catalyzed by Cu2+ ions,8-10 in search of factors causing the formation of spatiotemporal patterns in this system according to our previous report.11 The BZ reaction is particularly convenient as the test system because the evolution of thermal fronts can be easily compared with the visual development of concentration fronts, particularly if ferroin is used as a catalyst. Furthermore, the mechanism of formation of such patterns in excitable BZ media is quite well understood and allows one to construct the model supporting the experimentally reported temperature distribution. 2. Experimental Methods 2.1. Reagents and Apparatus. For the BZ process, pure for analysis (p.a.) KBrO3 (POCh), KBr (POCh), Ce(NO3)3 · 6H2O (puriss., Merck), and 95% sulfuric acid (p.a, Chempur, Poland) were used without further purification. Malonic acid (p.a., CH2(COOH)2, Reachim, SU) was purified by recrystallization from p.a. acetone (Chempur). Monobromomalonic acid (BMA) was prepared ex tempore according to the following procedure: the mixture of 33 cm3 2 M KBr, 50 cm3 2 M malonic acid, and 55 cm3 6 M sulfuric acid was slowly titrated with saturated aqueous solution of KBrO3 until elemental bromine stopped developing, indicating full consumption of Br- ions in reaction with (excess) BrO3-. Solution of ferroin (0.025 M) was prepared by dissolution of 0.99 g of p.a. Fe(NH4)2(SO4)2 · 6H2O (POCh) and 1.49 g of p.a. 1,10-phenanthroline (POCh) in a 100 cm3 volumetric flask. For the oxidation of thiocyanate ions with hydrogen peroxide, p.a. NaSCN (Fluka, Poland), p.a. NaOH (Merck, Germany), p.a. 95% (w/w) H2SO4 (POCh, Poland), p.a. CuSO4 (POCh, Poland), and p.a. 30% H2O2 (Chempur, Poland) were used without further purification. For all solutions, triply distilled water, additionally purified in a final step using Millipore filters, was used. Silica gel, fumed (particle size 0.007 µm, 390 ( 40 m2 g-1) manufactured by Sigma, was used to enhance the viscosity of the medium for the reaction performed in the thin-layer reactor. Infrared thermography measurements were performed for the thin-layer of the solution in an uncovered Petri dish at an ambient temperature of 294 ( 0.5 K. For BZ process, the spontaneous onset and evolution of blue concentric traveling fronts on a red background were recorded simultaneously with the optical digital camera (Nikon D90, resolution 5 million pixels) and the infrared camera (model ThermaCAM SC2000, manufactured by FLIR Systems AB, matrix 320 × 240 pixels, sensitivity 0.08 at 303 K). (See Figure 1.) For the thin-layer H2O2-NaSCN-NaOH-CuSO4 system, the visual observations were not carried out because the variations of the solution color were then practically undetectable. The raw infrared images were

Pekala et al.

Figure 1. Scheme of the experimental setup for simultaneous monitoring of the traveling fronts in the Belousov-Zhabotinsky reaction with the optical digital camera and infrared camera. The thermogram was focused on the upper free surface of the solution layer. During the analogous measurements for the H2O2-NaSCN-NaOH-CuSO4 system, the visual monitoring of the solution state was not possible because of undetectable color changes of the practically colorless solution.

processed using ThermaCAM Explorer 99 software to optimize optical visualization of temperature distribution without any changes to the original temperature values. For the studies of both oscillatory reactions under batch conditions, the Dewar vessel was used, the content of which was stirred with magnetic stirrer PM TYPE MM 6 (Poland). The measurements of bulk temperature variations were performed with the use of a high-precision centigrade temperature sensor LM35 (National Semiconductor) connected to 9 V power source and digital voltmeter type V533 (Meratronik, Poland), allowing us to detect temperature changes on the order of 0.01 K. Simultaneous measurements of the oscillatory variations of Pt electrode (A ) 0.6 cm2) potential were performed with a Hewlett-Packard 7090A multichannel measurement plotting system. The reference electrode Ag|AgSCN|0.1 M NaSCN was separated from the studied solution with a salt bridge filled with 0.1 M NaSCN. 3. Results of the Experiments and Numerical Modeling 3.1. Thermochemical and Potentiometric Studies of the BZ System. Before the presentation of the thermograms, one should realize that they show the temperature distribution on the surface, not in the bulk, of thin layer of the solution. For the purpose of simultaneous infrared and visual monitoring of the course of BZ process, it was carried out in a horizontal Petri dish of 79 mm diameter. The solutions of sat. KBrO3, freshly prepared bromomalonic acid, and ferroin (volume ratio 10:4:1) were poured into the Petri dish in the indicated order. The resulting solution was immediately stirred until the transient, uniformly distributed blue color returned to red. The thickness of the solution layer was ca. 2 mm. In the experiments involving silica gel medium, the Petri dish contained the gel powder prior

Monitoring Spatiotemporal Patterns

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7905

Figure 2. Comparison of the optical images and thermograms of the spatiotemporal pattern formation in the BZ reaction occurring in the thin layer (d ) 2 mm) of aqueous solution placed in a Petri dish. In the thermogram, temperature increases from blue, through yellow, to red color. (See the temperature scale.) Zones of the predominating oxidized (blue) form of the ferroin catalyst as well as regions through which the wave fronts propagated exhibit higher temperature than the external excitable surroundings. The indicated wave pattern developed after 86 s, following mixing of the reactants (with the first blue dot in red medium detected optically after 68 s).

to pouring of all solutions, and the resulting mixture was homogenized. For the aqueous (i.e., silica-gel-free) reaction medium, the development of randomly born circular blue concentration fronts on red background was accompanied with simultaneous (visualized by infrared camera) temperature inhomogeneities, exhibiting correlation with the morphology of the concentration fronts. The areas encircled by blue wave fronts (zones of predominance of Fe(III) complex), that is, also including the inner red zones, remaining in the refractory state for some time, exhibited generally higher temperature than the external red areas of excitable medium not yet experiencing the excitation to the blue state (Figure 2). The local increase in temperature in the area of the wave fronts is qualitatively concordant with previous measurements.4,6 The persistence of higher temperature also in the inner area of the circular waves means that the solution does not undergo a detectable cooling due to contact of the solution surface with cooler environment, presumably because consecutive wave fronts maintain the enhanced temperature. The picture is, however, slightly distorted, presumably because of possible surface convection, driven by local gradients of surface tension as well as because of inhomogeneous surface evaporation of water and other volatile species (e.g., traces amounts of gaseous bromine) that is, however, insufficient to cool the inner areas of the circular waves. If analogous experiments are performed in the medium enriched with the silica gel, which hinders the convection and presumably also slows the surface evaporation, then the quality of thermograms appears to be significantly improved. Figure 3 collects representative results of the simultaneous visual and infrared monitoring of the evolution of traveling fronts in the BZ process running in such a medium. Because of the relatively large amount of silica gel, the visual image is slightly distorted and the image is not ideally transparent. Figure 3 shows that for the solution composition studied by us, the maximum reported temperature difference is close to 0.2 K. Compared with Figure 2, the results with silica gel show that the internal (optically red) areas of the concentric waves exhibit still enhanced but slightly lower temperature than the areas of blue fronts, presumably due to certain cooling of the inner zones, which did not yet experience the birth and the propagation of secondary blue wavefronts.

Figure 3. Comparison of visual images and thermograms of the traveling chemical waves in the thin layer (d ) 1.8 mm) of the solution with BZ process occurring in an aqueous medium with an addition of ca. 3% (w/w) of fumed silica gel for the inhibition of convective motions. Bluish zones on red background in optical images correspond to yellow-green zones in the inner part of thermograms, indicating higher local temperature. The conditional zero of the time scale corresponds to the first pair of images shown.

Figure 4. Simultaneously measured oscillatory variations of the solution temperature (1) and Pt electrode potential (2) for the Belousov-Zhabotinsky (BZ) process carried out in the stirred batch reactor for the same initial concentrations of reactants as those in the infrared thermography experiments.

Because the infrared thermography visualizes only the surface distribution of temperature, to distinguish between the surface and bulk temperature dynamics, we recorded the temporary temperature variation for the stirred solution with BZ process. The dependence, shown in Figure 4, essentially concordant with previous literature reports,3 confirms the validity of the experimental equipment used by us. These results complete our

7906


Pekala et al.

experimental studies of thermochemistry of BZ reaction, considered a test system here. 3.2. Modeling and Interpretation of the Thermal Images for the BZ Reaction. Construction of the Oregonator-Based Model. To interpret at least semiquantitatively the thermogram as a source of information on the thermochemical characteristics of the BZ reaction, we constructed the numerical model, based on the well established Oregonator,12 both for the homogeneous system and for the system involving the diffusion transport of reagents under conditions of its excitable dynamic characteristics. The main goal of the analysis was to correlate the morphology of the thermograms with various assignments of the enthalpy effects to the particular (a, b, c) reaction steps of the Oregonator

{ {

k1

A + Y 98 X + P (a1)

a

k2

X + Y 98 2P

(a2)

k3

A + X 98 2X + Z (b1)

b

k4

2X 98 P + A

c

k5

Z 98 fY

(1)

(b2) (c1)

with A ≡ BrO3-, P ≡ HOBr, X ≡ HBrO2, Y ≡ Br-, Z ≡ Ce(IV), or [Fe(phen)3]3+, and f being the adjustable stoichiometric coefficient that is the bifurcation parameter. Previous assessments of enthalpy effects of selected steps of the FKN mechanism3,4 of the BZ reaction can be treated now as (otherwise useful) model approximate parameters because Oregonator is a simplified version of the FKN model. For the integration of the differential equations of the Oregonator (stiff system), the modified simple Euler algorithm, involving automatic time-step size correction, was implemented. This algorithm successfully replaced the classical Gear’s approach, offering instead much shorter computation time. This reduction of computation time was particularly important for the (described further) modeling of the development of spatiotemporal patterns in 2-D space. Incorporation of Thermochemical Effects into the Homogeneous Oregonator. According to literature suggestions,3,4 the overall exothermic effect of the BZ reaction, which can be estimated as, for example, equal to -535 kJ for the malonic acid, and for the reaction stoichiometry given by Oregonator, is largely determined by the relatively high negative enthalpy of that reaction in the FKN model that corresponds to the simplified process (c1) in the Oregonator. Compared with that effect, the enthalpies of other FKN processes, as being ca. one order of magnitude lower, were considered negligible in the assessment of the overall reaction enthalpy. Because Oregonator is not directly equivalent to the FKN model, in the present calculations we ascribed the same heat effect to various reaction steps with the intention to study the role of their kinetics in the dynamics of heat evolution during the course of the BZ reaction. Because of the irreversible character of all reaction steps in the Oregonator, the temperature increase, dT, at every time step, dt, was calculated from the actual rate of a given process, to which appropriate molar heat effect was ascribed. For example,

Figure 5. Comparison of the dynamics of (A) X, Y, and Z species concentrations and (B) solution temperature, modeled for the Oregonator mechanism of BZ reaction. (B) The same heat effect -535 kJ was ascribed to the steps: (1) a1, (2) a2, (3) b1, (4) b2, and (5) c1 of the Oregonator (eq 1). In calculations of ∆T, the heat capacity of the solution was assumed to be equal to that of pure water (4.18 J/(g K)). Parameters: [A] ) 0.06 mol dm-3, k1 ) 2.1 dm3 mol-1 s-1, k2 ) 2 × 109 dm3 mol-1 s-1, k3 ) 1 × 104 dm3 mol-1 s-1, k4 ) 4 × 107 dm3 mol-1 s-1, k5 ) 0.5 s-1, f ) 2. Initial values: [X]0 ) 1.89 × 10-10, [Y]0 ) 1.0 × 10-7, [Z]0 ) 2.27 × 10-7 mol dm-3.

for the heat effect of ∆H ) -535 kJ mol-1 ascribed to the steps (a2) or (c1), the temperature increases were calculated according to the following formulas, respectively

dT ) |∆H|k2[X][Y] dt/Cs

(2a)

dT ) |∆H|k5[Z] dt/Cs

(2b)

where Cs is the heat capacity of the solution, approximated here as a specific heat capacity of water of a density 1 kg dm-3, that is, Cs ) 4.18 kJ dm-3 K-1. Figure 5B shows the staircase dependences of the solution temperature on time, similarly as the experimental courses3,4 but with different dT/dt slopes and ∆T amplitudes, correlating with the analogous d[X]/dt, d[Y]/dt, or d[Z]/dt slopes in Figure 5A. The highest dT/dt slopes, observed if the entire heat effect is ascribed either to (b1) or (b2) steps, associated with the autocatalytic X species (HBrO2), are not observed in the experiment; therefore, these cases have to be considered purely hypothetical. A significantly lower dT/dt slope occurs for the heat effect ascribed either to (a1) or (a2) or to (c1) step. In



concordance with the literature suggestions,3 the latter case should be the closest to the thermochemical characteristics of the real BZ system, with others cases remaining only hypothetical temperature variations. In this way, the validity of calculations of homogeneous temperature variations in terms of the Oregonator model is confirmed. Following these calculations, one can now extend the model to the 2-D system with diffusion and compute model temperature distribution associated with the onset and evolution of spatiotemporal patterns. Incorporation of Thermochemical Effects into the Oregonator with Diffusion. For the calculation of the diffusion progress, the model 2-D quadratic reaction space, consisting of 633 × 633 elements and corresponding to the 2 × 2 cm size of a real system, was assumed. To every differential equation of the Oregonator, the term Di(∂2[i]/∂x2 + ∂2[i]/∂y2), with i ) X, Y, or Z, respectively, was added. For every time step (∆t) of the diffusion progress, the explicit finite difference method was used,13 requiring the stability condition βi ) Di∆t/(∆x ) ∆y)2 e 0.5, which, in our case, to obtain quasi-circular and not rather quadratic model waves, had to be as small as 0.005. This procedure was followed by calculation of the advancement of all kinetic processes within the time step ∆t. Figure 6A shows the modeled map of the spatial distribution of the concentration of species Z (i.e., oxidized form of a catalyst). The scheme of color encoding was chosen so that this model picture reminds us of the natural colors of the BZ system in the Petri dish. This plot should be compared with the distribution of temperature, visualized in Figure 6B, and obtained for the entire reaction enthalpy ascribed to step (c1) of the Oregonator (eq 1). The validity of our calculations is confirmed by comparison of the velocity of the model wavefronts propagation with theoretical predictions for the FKN mechanism,14,15 adapted here for the Oregonator model

Vfront ) 2(Dk[BrO3-][H+])1/2 ) 2(Dk3[A])1/2

(3)

where D is the diffusion coefficient of HBrO2 and k is the rate constant of the autocatalytic HBrO2 formation in the FKN model. The velocity of propagation of the model waves from Figure 6 equals 0.93 ( 0.05 mm s-1, which is quite close to the theoretical value of 1.1 mm s-1, predicted by eq 3 for k3 ) 1 × 104 M-1 s-1 and [A] ) 0.06 M. When comparing the ideal (circular) and model (angular) wavefronts, it is useful to remember that the velocity of the front propagation depends on the radius of curvature (r):16,17 V ) V0 - D(1/r), so the model wave should propagate more slowly because of higher local curvature. Our results deepen the thermochemical characteristics of the BZ reaction, used here as a test system. Analogous thermochemical studies were further performed for the H2O2SCN--OH--Cu2+ oscillatory system. 3.3. Thermochemical and Potentiometric Studies of the H2O2-NaSCN-NaOH-Cu2+ System. As for the BZ system, infrared thermography experiments were performed for aqueous media without and with the addition of silica gel to distinguish between the convection-driven and convection-less patterns. In the first case, the solutions of 0.1 M NaSCN and 0.1 M NaOH were first mixed, and then the solutions of 9.8 M H2O2 and 0.02 M CuSO4 were added to achieve the following initial concentrations in the reaction mixture: [NaSCN]0 ) 0.051 M, [NaOH]0 ) 0.045 M, [H2O2]0 ) 0.34 M, [CuSO4]0 ) 2.1 ×

Figure 6. Modeled 2-D maps of (A) the concentration distribution of species Z in the Oregonator and (B) the corresponding temperature distribution for the heat effect -535 kJ ascribed to step (c1) of the Oregonator (cf. eq 2b). (C) Temperature profile T ) f(x) corresponding to part B for fixed y ) 0.8 cm. The parameters of the Oregonator model correspond to the excitable characteristics of the reaction medium, and the waves were induced by arbitrarily chosen local [Z] fluctuations. Total model time, tmax ) 7.5 s, was divided into N ) 750 time steps, giving time step ∆t ) 0.01 s. Parameters of the excitable chemical system: [A] ) 0.06, k1 ) 2.1 dm3 mol-1 s-1, k2 ) 2 × 109 dm3 mol-1 s-1, k3 ) 1 × 104 dm3 mol-1 s-1, k4 ) 4 × 107 dm3 mol-1 s-1, k5 ) 0.5 s-1, f ) 2. Initial values: [X]0 ) 1.89 × 10-10 mol dm-3, [Y]0 ) 4.5 × 10-7 mol dm-3, [Z]0 ) 2.27 × 10-7 mol dm-3. Parameters of the diffusion system: xmax ) ymax ) 2 cm divided into MX ) MY ) 0 to 632 spatial steps ∆x ) ∆y, DX ) DY ) DZ ) 5 × 10-6 cm2 s-1, β ) 0.005. Model perturbation were introduced in a form of [Y] ) 1 × 10-7 M, being ca. 1/4 of the steady-state concentration of Y, imposed into two single spatial cells of the coordinates: (Mx, My) ) (259, 259) at t ) 0 s and (Mx, My) ) (449, 449) at t ) 3.0 s.

7908


Pekala et al.

Figure 7. (A) Thermograms of the uncovered surface of the thin layer of the solution with the oscillatory catalytic oxidation of thiocyanate ions with hydrogen peroxide, (B) corresponding temperature scale, and (C) time scale, that is, the dependence between the image number and time measured from the moment of mixing of all the reagents.

10-4 M. The mixture was then poured in an uncovered Petri dish, and thermograms were recorded every 20 s. Representative set of such images is shown in Figure 7A, with the temperature and time scale shown in Figure 7B,C, respectively. The total time of this experiment, exceeding 0.5 h, is sufficient to complete the entire process on its way toward the final equilibrium state. Therefore, it is easy to understand that the decrease in the temperature at the final pictures to the values comparable to those for the first pictures is caused by trivial cooling of the solution layer in contact with the surroundings at the end of the reaction course. In turn, the increase in the temperature observed between consecutive minima and maxima is due to the exothermicity of the studied process. During its course, the surface inhomogeneities of the temperature distribution, which can be a potential source of surface instabilities, are clearly observed. Also, the nonmonotonic variations of the

temperature in the same place of the solution are clearly visible. For example, image 42 is followed by the series of images 43-55, which indicate lower temperature of almost the entire surface, before it rises again, as image 58 proves. The period of thermal oscillations visualized by infrared thermography (ca. 4 min.) is close to the period of the Pt electrode potential oscillations (ca. 3 min.), determined under conditions of the bulk stirred reactor. (The difference might be caused by not identical temperature of both solutions.) However, an attempt to explain these temperature variations in terms of periodic predomination of endothermic reaction steps, for the oscillatory process that should be effectively dissipative, seems to be controversial. The problem, whether it is only a surface effect or also a bulk property of the studied system, can be resolved only by comparison of the thermograms with the measurements of the temperature variations of the bulk of the stirred solution.



Figure 8. (A) Thermograms of the surface of the thin layer of the solution with the oscillatory catalytic oxidation of thiocyanate ions with hydrogen peroxide running in the presence of ca. 4% (w/w) of fumed silica gel, (B) corresponding temperature scale, and (C) the time scale, measured from the moment of mixing of all reagents.

7910


Figure 9. (A) Simultaneously measured oscillatory variations of the solution temperature T (1) and Pt electrode potential E (2) for the oscillatory, Cu(II)-catalyzed oxidation of thiocyanates with hydrogen peroxide, carried out in the stirred batch reactor, for the initial concentrations of reactants: [NaSCN]0 ) 0.097 M, [NaOH] ) 0.086 M, [H2O2]0 ) 0.67 M, [CuSO4]0 ) 4.1 × 10-4 M. (B) Enlarged part of A, comparing variations of temperature T (1), its time derivative dT/dt (2), and Pt electrode potential E (3), showing locally higher dT/ dt slopes (indicated by vertical arrows) in the area of potentiometric peaks.

In the next series of infrared thermography experiments, the same initial reactant concentrations were used, but the solution also contained ca. 4% (w/w) of fumed silica gel for the hindrance of convection, as for the BZ system. Figure 8 collects a representative set of thermograms, together with the corresponding temperature and time scale. At conditional “zero time” of recording of the images, the solution is already heated, and the following images indicate certain inhomogeneities in the surface temperature distribution until the reaction layer cools in contact with surroundings because of the reaction completion. In this case, the periodic cooling/heating of the reaction mixture is less pronounced, although it still remains observable: images numbers 26 and 37/39 exhibit a bit lower average temperature than the neighboring pictures. As for the BZ system, the understanding of both thermogram sequences for the H2O2-SCN--OH--Cu2+ system requires their comparison with the simultaneous measurements of the temperature and Pt electrode potential variations under the conditions of the stirred batch reactor (Figure 9). To detect eventual subtle temperature changes, the concentrations of the reactants were for this purpose doubled, compared with the concentrations used for infrared thermography experiments. Figure 9 shows that the studied process is more exothermic than the BZ reaction: over ca. 10 min, the entire system’s

Pekala et al. temperature increases for ca. 7.5°. Careful analysis of the temperature increase indicates its locally enhanced slope within the area of the potentiometric peak. Finally, no cooling of the reaction mixture, at any time, was observed, which means that such cooling, reported in infrared thermography experiments should be interpreted as a surface effect rather than caused by the contact of the solution surface with the cooler environment or perhaps also by the evaporation of periodically forming volatile reaction products that are, however, difficult to identify unambiguously. 3.4. Modeling of the Thermochemical Characteristics of the SCN--H2O2-OH--Cu2+ System. To explain the variations of bulk temperature of the solution in which the catalytic, oscillatory oxidation of thiocyanate ions with hydrogen peroxide occurred, we used our simplified, ninevariable model of this process, elaborated previously for the explanation of the potentiometric response of various inert electrodes.10 This explanation should indicate the reaction steps responsible for both the quasi-linear increase in temperature and the subtle, fast temperature increases within the area of potentiometric peaks. Quite logically, the overall significant rise in temperature should be ascribed to the reactions consuming large amount of reactants and yielding large amounts of final reaction products, according to the overall reaction scheme:8 4H2O2 + SCN- f HSO4- + NH4+ + HCO3- + H2O. In terms of our simplified mechanism, the following possibilities can be considered. The appropriate heat effect can be ascribed, for example, to reaction step M5, in which main reactant (H2O2) is consumed. (We keep here the original notation of equations used in the most advanced mechanism of this process.9)

H2O2 + SCN- f (OSCN- f OOSCN-) + H2O (M5) For a sufficiently large reaction enthalpy ∆HM5 ) -600 kJ, one obtains the quasi-linear temperature increase of 9° within 1500 s. Alternatively, if the same heat effect is ascribed to reaction step M8, producing the main product (SO42-)

OOSCN- + OOS(O)CN- + [OH-] f (OSCN- f OOSCN-) + SO42- + HOCN (M8) then the quasi-linear temperature increase within the same time interval covers ca. 3°. Next, the subtle, fast local temperature increases within the areas of the potentiometric peak should be ascribed, in our opinion, to the reaction step involving the species forming autocatalytically, which is O(SO)CN- engaged in reaction step M21

OS(O)CN-+HO2 · f SO3 · - + HOCN

(M21)

In terms of this concept, semiquantitative concordance between the experimental and model temperature dynamics (cf. curves 1 and 2 in Figure 10) one obtains under assumption that the enthalpy of this process is close to ∆HM21 ) -1500 kJ. Strictly speaking, this heat effect can be ascribed not solely to the single M21 step but can be considered to be a summary enthalpy of reaction M21 and the following rapid processes, for example, involving practically diffusion-


J. Phys. Chem. A, Vol. 114, No. 30, 2010 7911 infrared camera reports only the surface distribution of temperature and on the solution surface additional process of the exchange heat/matter with the surroundings can occur. In this stage of studies, it is too early to model the spatiotemporal temperature patterns for the H2O2-SCN--OH--Cu2+ system, because the origin of chemical waves, recorded for the thin layer of the solution placed between two glass plates,11 still remains unclear. In further studies, it will be useful to consider, among others, the interactions between the chemical waves and hydrodynamic flows, described by Mu¨ller et al. in a series of papers.18-22 Therefore, results presented in this article have to be developed into further seeking of the mechanism causing the spatiotemporal patterns in the H2O2-SCN- oscillator.

Figure 10. Comparison of the simulated increase in the solution temperature T (1) and its time derivative dT/dt (2) with the simulated oscillatory variations of the (mixed) Pt electrode potential Emixed (3) for the nine-variable kinetic model of the H2O2-SCN--OH--Cu2+ system. Constant concentrations [OH-] ) 0.001 M, [H2O2] ) 0.585 M, [HO2-] ) 0.085 M, [SCN-] ) 0.097 M, [Cu] ) [Cu(SCN)2-]0 ) 4.1 × 10-4 M. Other parameters of the nine-variable model (rate constants) as in ref 10. Reaction enthalpies ∆HM8 ) -600 kJ/mol and ∆HM21 ) -1500 kJ/mol. Electrochemical characteristics for the mixed potential (Emixed): for Cu(OH)3-/Cu(OH)2- redox couple: formal potential E10′ ) -0.3 V, heterogeneous standard rate constant ks,1 ) 1 cm s-1; for HO2•/HO2- redox couple: E20′ ) 0.23 V, ks,2 ) 1 × 10-4 cm s-1.

controlled recombination of SO3•- radicals to SO42- and SO32- ions, denoted as reaction M23 step

2SO3 · - + [2OH-] f SO42- + SO32- + H2O

(M23) with (due to large OH- excess) the pseudo-second-order rate constant kM23 ) 1 × 108 dm3 mol-1 s-1. Furthermore, using our previous approach,10 one can calculate theoretical oscillatory variations of the mixed potential of Pt electrode, with the peaks exhibiting correlation with the enhanced local dT/dt slopes of the temperature variations (cf. curve 3 in Figure 10). Some quantitative discrepancies between experimental and theoretical courses (e.g., between the oscillation periods) are presumably due to the inevitable simplifications embedded in our nine-variable kinetic model10 compared with high complexity of the real H2O2-SCN--OH--Cu2+ system. Nevertheless, for the parameters used, the temperature increase per every oscillation period remains in quite a good concordance with the experiment. 4. Conclusions In conclusion, our thermochemical experiments supported by model calculations allowed us to ascribe reaction enthalpies to the appropriate reactions steps that appear to be important for the explanation of the observed dependences of the solution temperature on time. Concerning the infrared thermography experiments, results for the BZ system show that this method can be useful for the identification of the temperature gradients that can contribute to the driving forces for the spatiotemporal patterns. However, as our studies for the H2O2-SCN-OH--Cu2+ oscillator prove, the interpretation of thermograms images can be ambiguous, and in every case, the infrared thermography response should be confronted with the temperature dynamics for the bulk, stirred sample. This is because the

Acknowledgment. This scientific work was financed through the research grant N N204 242134 from the Ministry of Science and Higher Education, Poland, for the years 2008-2011 for the research project. We thank Mr. Maciej Feszczuk, M.Sc., electronic engineer for constructing the high-sensitive temperature sensor. References and Notes (1) Pojman, J. A.; Epstein, I. R. J. Phys. Chem. 1990, 94, 4966–4972. (2) Bo¨ckmann, M.; Hess, B.; Mu¨ller, S. C. Phys. ReV. E 1996, 53, 5498–5501. (3) Ko¨ro¨s, E.; Orbań, M.; Nagy, Z. Acta Chim. Acad. Sci. Hung. 1979, 100, 449–461. (4) Field, R. Experimental Characteristics and Mechanism of Chemical Oscillations and Travelling Waves in Bromate-Based Closed Systems. In Oscillations and TraVelling WaVes in Chemical Systems; Field, R. J., Burger, M., Eds.; Wiley-Interscience: New York, 1985; pp 75-116 (Russian translation: Mir: Moscow, 1988). (5) Lamprecht, I.; Schaarschmidt, B. Thermochim. Acta 1978, 22, 257– 266. (6) Nagy-Ungvarai, Z.; Mu¨ller, S. C.; Tyson, J.; Hess, B. J. Phys. Chem. 1989, 93, 2760–2764. (7) Wood, P. M.; Ross, J. J. Chem. Phys. 1985, 82, 1924–1936. (8) Orbań, M. J. Am. Chem. Soc. 1986, 108, 6893–6898. (9) Luo, Y.; Orbań, M.; Kustin, K.; Epstein, I. R. J. Am. Chem. Soc. 1989, 111, 4541–4548. (10) Wisńiewski, A.; Pekala, K.; Orlik, M. J. Phys. Chem. A 2010, 114, 183–190. (11) Pekala, K.; Jurczakowski, R.; Lewera, A.; Orlik, M. J. Phys. Chem. A 2007, 111, 3439–3442. (12) Field, R. J.; Noyes, R. M. J. Chem. Phys. 1974, 60, 1877–1884. (13) Crank, J. The Mathematics of Diffusion, 2nd ed.; Clarendon Press: Oxford, U.K., 1975. (14) Tyson, J. Quantitative Description of Oscillations, Bistability and Travelling Waves in the Belousov-Zhabotinsky Reaction. In Oscillations and TraVelling WaVes in Chemical Systems; Field, R. J.; Burger., M., Eds.; Wiley-Interscience: New York, 1985; pp 117-166 (Russian translation: Mir: Moscow, 1988). (15) Gray, P.; Scott, S. K. Chemical Oscillations and Instabilities; Clarendon Press: Oxford, U.K., 1990. (16) Epstein, I. R.; Pojman, J. A. An Introduction to Nonlinear Chemical Dynamics. Oscillations, WaVes, Patterns, and Chaos; Oxford University Press: New York, 1998. (17) Schneider, F. W.; Mu¨nster, A. F. Nichtlineare Dynamik in der Chemie; Spektrum Akad. Vlg.: Oxford, U.K., 1996. (18) Miike, H.; Mu¨ller, S. C.; Hess, B. Chem. Phys. Lett. 1988, 144, 515–0520. (19) Miike, H.; Mu¨ller, S. C.; Hess, B. Interaction of Chemical Waves and Hydrodynamics Flow. In CooperatiVe Dynamics in Physical Systems; Takayama, H., Ed.; Springer-Verlag: Berlin, 1989; pp 328-329. (20) Plesser, T.; Miike, H.; Mu¨ller, S. C.; Winters, K. H. Propagating Chemical Waves and Their Relation to Hydrodynamic Flow. In Spatial Inhomogeneities and Transient BehaViour in Chemical Kinetics; Gray, P., Nicolis, G., Baras, F., Borckmans, P., Scott, S. K., Ed.; Manchester University Press: New York, 1990; pp 383-391 . (21) Matthiessen, K.; Wilke, H.; Mu¨ller, S. C. Phys. ReV. E 1996, 53, 6056–6060. (22) Steinbock, O.; Kasper, E.; Mu¨ller, S. C. J. Phys. Chem. A 1999, 103, 3442–3446.

JP104299A

Monitoring of Spatiotemporal Patterns in the Oscillatory Chemical

Recommend Documents