J. Phys. Chem. 1991,95, 5831-5837
5831
radical of acridine has an absorption maximum in the 55woO-nm regional6The pK, of the acridine radical is apparently above 1416f so that, in protic solvents, it should be difficult to distinguish between triplet quenching by direct hydrogen atom transfer and triplet quenching by electron transfer followed by rapid proton transfer. The kinetic isotope effects observed by Kuz'min et al. indicate that direct hydrogen atom transfer occurs in some cases? Kaye and Stonehil122studied the electrochemistry of acridine in aqueous ethanol, where El is pH-dependent. At pH 8.3 the half-wave potential is 4 . 7 9 versus SCE, which corresponds to an E l I 2of 4 . 5 5 V versus NHE. This is the same value as the one estimated for HAcrC0O'- on the basis of its reactivity with bipyridinium compounds (Figure 4). The acridine radical reduces 9, IO-anthraquinone-2-sulfonatein basic aqueous solution with a rate constant of 4.5 X IO9 M-' s-*, which is close to the diffusion-controlled value.I6' This number is also close to the limiting value observed for the reduction of bipyridinium acceptors of HAcrC0O'- (Figure 4). Comparison of the value of @T-R for MV'+ formation to that for the formation of HAcrCOO- shows that HAcrC0O'- reduces MV2+ to M V + with 90-100% efficiency. The absorption spectrum of the Trolox radical obtained in this study has an absorption maximum and shape that are characteristic of the published spectra of this radicalI5 as well as the radicals of a-toco hero1 (vitamin E) and closcly related compounds in polar solvents. There is considerable variation in the extinction
coefficient at A- for these radicals, however, with values ranging from 4000 to 7100 M-' cm-'. The value of 7200 f 300 M-' cm-I at 432 nm found in this study is essentially the same as that reported by Davies et a1.I" and within 10%of the value reported by Thomas and Bie1ski.lM The fact that the value of @T4R that is obtained for eq 1 on the basis of change in absorbance at 440 nm is within experimental uncertainty of the value obtained at 510 nm, where TxO' does not absorb, indicates that the extinction coefficients of TxO' and HAcrC0O'- used to calculate @T+R (Table 11) are not far from the actual values.
(22) Kaye, R. C.; Stonehill, H. 1. J . Chem. Soc. 1951, 27-38. (23) (a) Simic, M.G.; Hunter, E. P. L. In Oxygen Radicals in Chemistry and Biology;Bors, W., Saran, M.; Tait, D., Eds.;de Gruyter: Berlin, 1984; pp 113-120. (b) Mukai, K.; Watanabe, Y.; Ishizu, K. Bull. Chem. Soc. Jpn. 1986,59.2899-2900. (c) Simic, M. G.; Jovanwic, S. V. In Irh Inrernarional Congress on Oxygen Radicals; Organized by the National Bureau of Standards, University of California at San Diego, La Jolla, California, June 27-July 3, 1987; pp 34-35.
Acknowledgment. We are grateful to William M. McGowan for providing samples of TriQ2+,TetraQ2+,and DMTetraQ2+. This work was supported by the Basic Energy Sciences division of the Office of Energy Research, U.S.Department of Energy (Grant DE-FG02-88ER13492) and by the Center for Photochemical Sciences at Bowling Green State University.
d
B
Conclusion This study and our earlier one have confirmed that AcrCOOcan substitute for AntCOO- as an efficient mediator of photosensitized electron-transfer reactions via the triplet state. AcrCOO- is significant as an alternative to AntCOO- because AcrCOO- tends to act via a reductive quenching mechanism whereas AntCOO- tends to act via an oxidative quenching mechanism. The fact that the triplet quantum yield of AcrCOOis relatively low in aqueous media does not impede its use in artificial photosynthesis since the triplet state can be efficiently generated with dyes such as Ru(bpy)?+. The HAcrCOO' radical is sufficiently stable that it may be useful as a reductant without the intervention of an acceptor such as MVZ+.
Gel Systems for the Belousov-Zhabotlnskii Reaction T.Yamaguchi,t L. Kuhnert,t Zs. Nagy-Ungvarai,* S. C. Muller, and B. Hess Max-Planck-lnsritut fur Ernahrungsphysiologie, Rheinlanddamm 201, W-4600 Dortmund 1 , FRG (Received: December 19, 1990)
Gel systems and their advantages over an aqueous system for spatial patterns in the Belousov-Zhabotinskii reaction are investigated. Five new gel preparations are introduced in which several ferroin-type catalysts (highly hydrophobic and anionic) are immobilized. Together with previously known systems these are classified into three categories: soluble, immobilized continuous, and immobilized discrete systems. The use of highly hydrophobic and anionic BZ catalysts is reported for the first time. Some observations on pattern formation in seven different gel preparations are described and further possibilities for the use of these gel systems are pointed out.
Introduction Most experiments on spatial pattern formation in the Belousov-Zhabotinskii (BZ) reaction have been carried out in homogeneous aqueous solutions.' An early work2 describing pattern formation in the BZ reaction in a gelled medium (a collodion film) in which the catalyst ferroin was immobilized has remained a curiosity for a long time. After this work Winfree carried out two foresighted experiments using Millipore filters) and Aerosil (Degussa)' in order to eliminate hydrodynamic effects from the reacting media. These media are, however, not transparent for optical observation. 'Permanent addnss: National Chemical Laboratory for Industry, Higaahi
1-1, Tsukuba, lbaraki 305, Japan.
$Present address: Technische UniversitHt Berlin, Institut far Technische Chemic, TC3, Strasse des 17. Juni 135, W-lo00 Berlin 12, FRG.
0022-3654/91/2095-5831$02.50/0
Nowada s there is a growing interest for working with gel systems,51Jmotivated by several explicit advantages which they (1) Ross, J.; Mtlllcr, S. C.; Vidal, C. Science 1988, 210, 460. (2) De Simone, J. A.; Beil, D. L.; Scrivcn, L. E. Science 1973, 180, 946. (3) Winfree, A. T. Sci. Am. 1974, 230, 82. (4) Winfree, A. T. The Geometry of Biological T h e ; Springer: Berlin, 1980; p 301. (5) Kuhnert, L. Natunvissenschaften 1983, 70, 464. (6) Noszticzius, Z.; Horsthemke, W.; Mc. Cormick, W. D.; Swinney, H. L. Nature 1987, 329, 619. (7) Maselko, J.; Reckley, J. S.;Showalter, K. J . Phys. Chem. 1W9, 93, 2774. (8) Maselko, J.; Showalter, K. Narure 1989, 339, 609. (9) Jahnke, W.; Skaggs. W. E.; Winfree, A. T. J . Phys. Chem. 1989,93, 740. (10) Agladze, K. 1.; Krinsky, V. 1.; Panfilov, A. V.; Linde, H.; Kuhnert, L. Physica D 1989, 39, 38.
0 1991 American Chemical Society
5832 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 TABLE I: Gel Syctem for the Belourov-Zhrbotimki ReactiM catalyst Fe(pha&
Fe( batho),
a For
soluble immobilized system system continuous continuous discrete Millipore3 collodion2 cation-exchange resin7,* Acrosil' silica gello agar-agars (water glass) acrylamide6 acrylamide silica gel alginate silica gel (water glass) anion-exchange resin
structure and properties of the catalysts sec Table 11,
offer. In the present paper we summarize these advantages, introduce several new gel systems for the BZ reaction catalyzed by new ferroin-type catalysts, classify the gel systems into three categories, and describe the new methods of their preparation. Furthermore, we show some observations on pattern formation in them, in connection with the effect of immobilization of catalyst, net charge of gels, and condition of gels (continuous or discrete). Finally, open and newly introduced problems are briefly described.
Why Gel Systems? The explicit advantages of using gels instead of aqueous systems are as follows: 1. Hydrodynamic convection is eliminated in gel systems. In aqueous fluid systems, on the other hand, there may appear macroscopic flow or turbulence due to surface cooling with evaporation or spatial inhomogeneitiesof chemical species caused by the propagation of BZ waves. This hydrodynamic effect sometimes brings about spatially stationary structure^'^ and perturbs the initial spatial patterns to bifurcate into more complex structures. Macroscopic flow coupled with chemical reaction was observed even in a thin aqueous layer (thickness ca. 0.85 mm) with a liquid-gas interface excluding evaporation14 or under completely covered condition^.'^ It is obvious that theoretical results dealing with reactionaiffusion systems, such as the Turing instabilities,I6'* are comparable only with results of experiments in which this hydrodynamic effect is carefully eliminated. Gel systems easily offer such an experimental condition. 2. Within a gel matrix a variety of chemical spccies--catalyst, substrates, charged groups-and even physical obstacles can be immobilized." Inhibitors or other substances can also be introduced at a well-defined location. In the present work, the following points are emphasized in connection with immobilization: (i) The catalyst can be immobilized by several new methods of preparation (see Table I). That means its diffusion coefficient is zero, whereas in aqueous solutions it has a finite value which, in theoretical descriptions of the BZ reaction,Igis regarded to be equal to the diffusion coefficient of the autocatalytic species (HBrOJ. As shown theoretically, the assumption whether the diffusion coefficient of the catalyst is zero or has a finite value can lead to essential differences in the properties of BZ reaction patterns." (ii) Charged gel matrices have some influence on the formation of the BZ patterns. The electrostatic interaction of ionic molecules (1 1) Kuhnert, L.;Krug, H.J.; Pohlmann, L. Nova Acta Leopoldina 1989, 61, 268. (12) Pertsov, A. M.;Aliev, R. R.; Krinsky, V. I. Nature 1990,345,419. (13) Orban, M.J. Am. Chem. Soc. 1980, 102,4311. (14) Miike, H.;Muller, S. C.; Hws, B. Phys. Lert. A. 1989, 141, 25. (IS) Rodriguez, J.; Vidal, C. J . Phys. Chem. 1989. 93, 2737. (16) Borckmans, P.; Dewel, G.; Walgraef, D.; Katayama, Y . J . Slur. Phys. 1987, 48, 1031.
(17) Forbes, L. K. Physica D 1990.43, 140. (18)Castets, V.; Dulos, E.;Boissonade, F.; DeKepper, P. Phys. Reo. Leu. 1990,64, 2933. (19)Keener, J. P.; Tyson, J. J. Physica D 1986, 21, 307. (20) Zykov, V. S. Simularion of wave processes in excitable media; Manchester University Press: Manchester, U.K., 1987.
Yamaguchi et al. with charged gels may produce changes in the diffusion coefficient, an effect that can possibly be varied systematically. 3. Gel systems, especially those with immobilized catalysts, offer a possibility to study chemical waves in open systems. Similarly to the continuous flow stirred tank reactor (CSTR) experiments in homogeneous liquid systems, continuous fluxes of reactants and products can be realized through the gel without disturbing the pattern forming in it? Moreover, steady concentration gradients can readily be maintained in such open gel systems. The openness of the system is one of the necessary conditions for achieving the Turing instabilities, too. Furthermore, the following new advantages should be pointed out, which have become clear in the present study. 4. Even water-insoluble catalysts, like Fe(batho)t+, can be studied in the BZ reaction after immobilization within or on a gel matrix. 5. The ferroin-type catalysts are more stable when futed in a gel than when solubilized in diluted sulfuric acid solutions in which they tend to decompose. Long-time behavior of patterns, for example, can be studied more easily in such gel systems. Until now such experiments have only been carried out in solutions containing Ce catalyst.21 6. Most of the gel materials offer bubble-free systems for hours due to their mechanical stiffness. Bubble formation in the BZ reaction is a disturbing problem in studying spatial patterns as bubbles interfere with pattern formation. Several bubble-free recipes have been but most gel matrices remain free from bubble formation even for the standard BZ reaction recipes.
Experimental Section Catalysts and Gel Systems. The new gel systems for the BZ reaction are summarized in Table I including also several systems that appeared in the previous literature. Three ferroin-type catalysts were examined (Table 11): Fe(phen)?' (ferroin), Fe( batho)t+, and Fe [batho(SO,),] ,&,where phen = 1 ,lo-phenanthroline, batho = 4,7-diphenyl-l,10phenanthroline (=bathophenanthroline), and b a t h ~ ( S O , ) = ~ bathophenanthrolinedisulfonate. Ferroin is a water-soluble catalyst and has an absorption maximum A, at 510 nm (6 = 11 100). It has been known as the only immobilized catalyst for the BZ reaction. Fe(batho)t+ and Fe[batho(SO,),],' are reported here for the first time. Both have ,A, at 533-535 nm, 25 nm higher than ferroin. Their molar absorption coefficients at ,A, reach ca. 22 000 which is twice as high as in case of ferroin.2s These spectrophotometric properties of the new catalysts are of a considerable advantage for the study of the BZ reaction because they are more sensitive and produce brighter color contrast during the change of the redox states than ferroin does. As bathophenanthroline is more hydrophobic than phenanthroline, Fe(bathe)?' is hardly soluble in water, whereas F e [ b a t h ~ ( S O , ) ~ ] , ~ is well soluble. This difference results from the presence of additional SO3-groups on bathophenanthroline. These negatively charged groups change the net charge of the catalyst from +2 to -4. Fe[batho(SO,),],' is the first example of a BZ catalyst that has a negative charge. Gel systems are classified into two large categories based on the condition of the catalyst: mobile or not mobile (soluble systems and immobilized systems, respectively, in Table I). In a catalyst-soluble gel system, not only the gel phase but also the surrounding aqueous phases, if present, can act as an excitable medium. In a catalyst-immobilizedgel system, however, only the gel matrix can be excitable and show some spatial or temporal patterns. Just by soaking it in a reacting solution, we can easily prepare an open excitable system. (21) Nagy-Ungvarai, Zs.;MOller, S.C.; Plesscr, Th.; Ha,B. Naiurwissenschafien 1988. 75, 87. (22) Bowers, P. G.;Caldwell. K. E.; Prendergrast, D. F. J. Phys. Chem. 1972, 76, 2185. (23)Salter, L. F.;Sheppard, J. C. In?. J . Chcm. Kinel. 1982. 14, 815. (24) Ouyang, Qi; Tam, W. Y.;DeKepper, P.; McCormic, W.D.; Noszticzius, Z.;Swinney, H.L. J . Phys. Chem. 1986, 91, 2181. (23) Schilt, A. A. Analyrical applicaiion of 1,lO-phenanthroline and teIated compounds; Pcrgamon Press: Oxford, U.K., 1969.
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5033
Gel Systems for the BZ Reaction TABLE 11: Catalysts for the Belousov-Zhabotinskii Reaction catalyst
ligand name and structure
charge ox/red
solubility in water
reduced catalyst Amex,
nm
e,
M-'cm-'
Fe(phen)3
phen = 1,lO-phenanthroline
+3/+2
high
5 10
11.ooo
Fe(batho),
batho = bathophenantroline= 4,7diphenyl-l,1Ophenanthroline
+3/+2
very low
533
22.400
-31-4
very high
535
22.100
Fe[b a t h ~ ( S O ~ ) ~ ] ~ batho(S03)2 = bathophenanthrdinedisulfonate
Depending on the condition of the gel medium in which the BZ reaction takes place, we can classify the systems further into two subgroups: continuous and discrete systems. Discrete gel systems are composed of gel particles whose diameter is very small compared to the wavelength of traveling chemical waves. The gel particles as a whole form a loosely coupled network through point contacts to the neighbors as well as through diffusion of chemical intermediates into the unexcitable aqueous medium between the particles. Preparation of Gels. Here we describe the recipes and some remarks for the investigated gel systems (a-g), including five new ones with immobilized ferroin-type catalysts (c-g). The gel a is the only "soluble" system examined in this work. The gels b-e belong to the "immobilized continuous" systems and the gels f and g to the "immobilized discrete" systems. ( a ) Ferroin Reaction Solution/Agar. The whole reaction solution including ferroin (solved in warm 1% agar solution) was gelled by cooling it down to room temperature, as was described earlier.5 Remark: Soluble system. Slightly turbid, soft gel. The only system with strong bubble formation in the gel at the concentrations used (cf. Figure 1). (6) Fe(phen),/Silica Gel (Water Glass). 15% aqueous sodium silicate, 25 mM ferroin, H20,and 1 M H2S04 were mixed in the composition of 10:2: 1:2. The solution was then poured into a Petri dish. The gelation took place slowly over ca. h. Before experiments were carried out, the gel was washed several times with 1 M H2SO4. During the washing procedure, part of the ferroin was removed from the gel. The amount of removed ferroin in the washing solution was determined spectrophotometrically and the concentration of ferroin immobilized in the gel was calculated. Remark: Transparent, fragile gel. It was first applied in ref 10. (c) Fe(batho),/Silica Gel (Water Glass). Because Fe(batho),S04 is hardly soluble in aqueous media, the immobilization was carried out after the preparation of silica gel. A mixed solution of 15% aqueous sodium silicate (5 mL), H 2 0 (1.5 mL), and 1 M H2S04(1 mL) was spread over a Petri dish of 70 mm in diameter and kept at room temperature for 12 h. Then, 5-10 mL 5 mM Fe(batho),S04 solution, dissolved in acetic acid, was poured on this silica gel. After another 12 h the catalyst solution was removed and the gel was washed thoroughly with H20. The concentration of the immobilized catalyst in the gel was 1 mM, which was determined by extracting it from the gel with acetic acid. Remark: Transparent, fragile gel. Its color contrast is brighter than that of ferroin/silica gels (b). (d) Fe(bath~)~/Poly(acrylamide).15% acrylamide gel (cross-linked with 0.4% Bis) containing 0.03% nonionic surfactant (NP-40, nonylphenylethylene oxide) was soaked in 2 mM Fe-
--
Figure 1. Traveling waves in agar gel (a) recorded by a 2D spectrophotometer system at X = 490 nm without using a diffuser. The rough structure on the surface of the gel and asymmetrical bubbles in the gel are observed. This roughness of the surface does not affect wave propagation, whereas the bubbles within the gel matrix cause local delays of the traveling waves.
(batho),S04 solution (in acetic acid) for 12 h. The red gel was then washed with water several times until the washing fluid became colorless. The concentration of the immobilized catalyst in the gel was 1 mM. Remark: Transparent, strong gel. Thickness is well controllable. (e) Fe(bath~)~/Calcium Alginate. 1 g of 3% aqueous solution of sodium alginate was spread on a plane glass plate (50 mm in diameter); then it was slowly put in contact with 5% aqueous Ca(N03)2. (The gelation takes place as a result of chelation of Ca2+ions by carboxylate groups in alginate.) After 15 min the calcium alginate gel was peeled from the glass plate and washed with water. The gel film was then soaked into ca. 5% Fe(batho),S04 solution (in acetic acid) for 12 h, followed by complete washing with water. Remark Clear, strong and elastic gel. Very thin films (down to 0.1 mm) can be produced. Fe(batho),S04 in acetic acid (2 (f) Fe(bath~)~/Silica-GeZ. mM) was adsorbed by silica gel (silica gel 60, Merck, 100-200
5834 The Journal of Physical Chemistry, Vol. 95, No. 15, I991
Yamaguchi et al.
mesh). This gel was ready for experiments after removal of acetic acid and subsequent washing with water. The amount of immobilized catalyst was 3 pmol/g of gel. Remark: Easy for preparation. Surface charge density is low compared with ionexchange resins. (g)Fe[bath~(SO~)~]~/Anion-Exchange Resin. 30 g of Dowex 1 X 4 (format form, 100-200 mesh) was suspended in 500 mL of water, and 10 mL of aqueous 25 mM Fe[batho(SO,),], (sodium salt) was added (8 pmol of catalyst/g of gel). Gentle stirring was carried out for 12 h. Adsorption of the catalyst was almost stoichiometrically achieved. After filtration the gel was washed with water and dried. Remark: Easy to prepare. Surface charge density is high and positive, which is opposite to cation-exchange resins.'~~ A prerequisite of using gel systems is that the lifetime of gels in the BZ medium must be longer than the time of observation for the reaction. It is fulfilled in all of our systems. The soluble gel (a) can be used only once for an experiment. All other gels (b-g) can be used even several times; after every experiment the gel must be washed clean with water and then kept under water or 25 mM H2S04 solution till the next experiment. Observation of Wave Propagation. For the observation of spatial patterns, the gel except for (a) was put into contact with an aqueous reaction mixture of NaBrO,, malonic acid, and H2S04. The concentration of all of the chemicals in the standard reaction mixture was 0.33 M. Occasionally, NaBr was added. For agar gel (a) all reactants were mixed together with agar to make one soluble phase (see preparation of gels). For velocity measurements in gel systems a and b a constant concentration of 60 mM NaBr (corresponding to a [BrMA] of 90 mM after the bromination reaction) was used. The concentration of NaBrO, and H2S04was varied from 0.2 to 0.6 M and from 0.2 to 1.O M, respectively. The concentration of the catalyst in the gel was varied from 1 to 5 mM. Some of the BZ reaction patterns observed in the gels were photographed directly. In other cases the patterns were recorded by our 2D spectrophotometricapparatus.26 In this apparatus the layer is normally illuminated with parallel light. However, to minimize the depth of field and avoid sharp imaging of a rough surface, as is shown in Figure 1, a diffuser plate was introduced into the optical path (Figure 2). Usually, patterns appear spontaneously in the gels, but they can also be triggered by touching the gel surface with a silver wire. On the other hand, inhibition of the wave propagation can be achieved by an iron wire. All experiments were carried out at room temperature (about 25 "C).
Results and Discussion The kinetics of the BZ reaction in gels is reflected by the velocity of the trigger waves u, which is mainly determined by the autocatalytic reaction step coupled with diffusion27 u
-
(kD[H+] [Br03-])1/2
where k is the rate constant of this step and D is the diffusion coefficient of the autocatalytic species. We measured the velocity of the first appearing circular wave in agar (a) and in silica gels (b) at different initial concentrations. There was no significant difference between the two sets of velocity data obtained in gels a and b. They were therefore combined to derive the following equation u (mm/min) = -0.85
+ 27.90([H+][Br03-])1/2
which is, within an error of a few percent, identical with the data found for aqueous solution^:^^*^^ u (mm/min) = -0.83
+ 27.87([H+] [Br03-])1/2
(26) Miiller, S. C.; Plesser, Th.; Hess, B. Nutuwissenschuften 1986, 73, 165. (27) Field, R. J.; Noyes, R. M.J . Am. Chem. SOC.1974, 96, 2001. (28) Nagy-Ungvarai, Zs.;Tyson, J. J.; Hess, B. J. Phys. Chem. 1989,93, 707 and references therein.
Figure 2. Irregular three-dimensional structure observed in silica gel (b) due to concentration-homogenizing process during which the reacting substances diffuse from the aqueous phase into the gel matrix.
This equality, first pointed out qualitatively in ref 5, reflects the facts that (i) diffusion coefficients of low-molecular-weightsubstances in diluted gels are comparable to diffusion coefficients in pure solutions, and (ii) the rate constant of the autocatalytic redox reaction is affected neither by the gel networks nor (iii) by the mobility of the catalyst (solubilized or immobilized). Pattern formation in agar gels (a) is very similar to the known cases in aqueous solutions. Concentric rings appear spontaneously or can be triggered by a silver wire immediately after the preparation of the gel, as the whole reaction solution is gelled. However, the study of patterns in agar gel systems is complicated because of the disturbing bubble formation at the studied concentrations, as shown in Figure 1. In all other continuous gels (b-e), where the catalyst is fixed, there is only a slow bubble formation in the later stages of the observation. In these cases the BZ waves appear after the reaction solution poured above the gel has diffused into the gel. During this diffusion process irregular three-dimensional structures evolve, closely related to the fact that the concentration of the reagents is different with varying depth of the gel. The duration of the period of irregular behavior varies
Gel Systems for the BZ Reaction
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5835
Figure 3. Double-armed spirals appeared spontaneously in poly(acry1amide) gel (d) which was suspended in the standard reacting solution.
from some minutes to more than 1 h depending on the initial concentration and the thickness of the gel. During this time the irregular patterns become increasingly regular, and after completion of the process of concentration homogenization, a coherent regular pattem dominates over the whole reaction territory. Such a process, observed in silica gel (b), is shown in Figure 2. A similar process can be observed when the reaction solution above a gel with a regular pattern is replaced by distilled water. In this case the chemicals BrOC, MA, BrMA, and H+ are diffusing into the water diluting this way their concentrations in the gel. After an irregular interval new regular patterns with concentric or spiral waves evolve which have larger wavelength corresponding to the decreased concentrations. In very thin gel layers (0.2-0.3 mm) with a large volume of reactant solutions at concentrations of [NaBrO,] < 0.3 M, [H2S04]< 0.4 M it was possible to reduce or avoid the chaotic diffusion stage. We could measure the velocity of the first wave in silica gels (b) only under such conditions. In regard to spontaneous pattern formation, mostly one-armed spiral waves are formed in gels. Occasionally, double-armed spirals are spotaneously produced in continuous silica gels (b) and poly(acry1amide) (d) at the standard concentrations as shown in Figure 3. In the discrete silica gel system (f) also three-armed spirals occur spontaneously, for example, for the reaction mixture [H2S04] = [NaBr03] = 0.28 M and [MA] = 0.56 M. These multiarmed spirals were previously prepared quite artificially in homogeneous, aqueous BZ reactions: two or more spiral centers had to be assembled together by an elaborate procedure.29 Spontaneous occurrence of multiarmed spirals in gel systems suggests that there are microinhomogeneities giving rise to several spiral centers, some of which happen to be located in a very close neighborhood. As we pointed out above, ferroin fixed in a gel is more stable against decomposition than in acidic aqueous solution. Therefore, long-time measurements can be easily carried out in gels. In a later stage of the reaction the composition of the system differs from the initial one, and due to a considerable decrease in excitability open ends of waves tend to shrink, as theoretically predicted in ref 30, instead of forming stable spirals which is characteristic for high excitability. A pattern due to low excitability observed in silica gel (b) is shown in Figure 4. The bubble breaks the wave front, and the open ends of the wave no more curl up to spirals but shrink in the lateral direction. The effect of the thickness of gels on the pattems was observed in case of alginate gel (e). A film of alginate gel (0.3 mm in thickness, concentration of immobilized Fe(batho), = 3 mM) was (29) Agladze, K. I.; Krinsky, V. I. Nature 1982, 296, 424. (30) Pertsov, A. M.; Panfilov, A. V.; Medvedeva, F. U. Biofizika 1983, 28, 100.
Figure 4. Broken wave front observed in silica gel (b) in the late stage of the experiment at low excitability.
suspended in the standard reacting solution and spiral patterns with wavelength of 0.82 mm appeared (Figure 5A). When the thickness of the gel was decreased to 0.2 mm, the color of the gel turned light brown without any pattern formation. However, addition of NaBr to the reacting solution was efficient for the formation of the BZ patterns when the thickness of the film was below the critical value (Figure 5B-D). In the range of initial concentrations of NaBr from 12 to 17 mM, a spiral-shaped BZ pattern with similar wavelength as in the thicker gel was observed (Figure 5C). Above a NaBr concentration of 33 mM, the color of the gel was bright red and the wavelength reached several millimeters (Figure 5D). These findings suggest the existence of a critical thickness of gels so as to produce the patterns. Below the critical thickness the rate of decrease in concentration of chemical intermediates (HBr02, Br-, and others) due to diffusion from both surfaces of the gel film exceeds their production rate, resulting in conditions where patterns cannot be formed. But diffusion of intermediates from the gel into the surrounding aqueous phase can be compensated by addition of NaBr to the reaction mixture. It increases the concentration of BrMA and therefore also that of Br- in the aqueous phase as well as in the gel. At such conditions the concentrations of the intermediates in the gel are kept at a higher level, above the critical concentration, which is necessary for chemical oscillation^.^^ Another possibility to control the diffusion or the localization of chemical species in the reaction mixture is provided by the use of charge immobilized in gel matrices (gels e and g). The outstanding effect of this electrostatic control was observed in gel g. Only 0.9% of the total positive charge on Dowex 1 X 4 is used for immobilization of F e [ b a t h ~ ( S O , ) ~and ] ~ therefore ~ the resin still keeps a highly positive charge density. In other words, the catalyst immobilized on the resin is densely surrounded by positively charged groups. Negatively charged species in the reacting media such as Br- and BrO; are concentrated close to the catalyst, whereas positively charged H+ is repelled. As a result, an electric double layer is formed close to the surface of the resin. In gel system g this electric double layer is an important reacting domain, which is deduced from the fact that considerably higher concentration of protons was necessary to produce the same BZ
(31) Kuhnert, L.; Agladze, K. I.; Krinsky, V. I. Nature 1989, 337, 244.
5836 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Yamaguchi et al.
A
A H+ Anion-exchange resin
B
y++ + a+--
Fe [ b a t h ~ ( S O ~ ) ~ ]
B
+ ,, A / Figure 6. (A) Target patterns appearing in the discrete anion-exchange resin (g). The composition of the reacting solution is [H,SO,] = 0.94 M, [malonic acid] = [NaBr03] = 0.125 M, [NaBr] = 12.5 mM. The wavelength of the tight patterns at the left side is about 1.2 mm. (B) Schematic drawing of a gel particle (g) with attracted and repelled ions.
C
D
Figure 5. (A) Spiral BZ patterns of wavelength of 0.82 mm observed in calcium alginate gel (e, thickness 0.3 mm) suspended in the standard reacting solution. (B-D) The influence of NaBr on the BZ pattern formation in gel films e with a thickness of 0.2 mm. The initial concentration of NaBr added to the standard reacting solution is 3.3 (B), 11.7 (C), and 33 mM (D), respectively.
pattern in anion-exchange resins than in neutral gel systems (Figure 6). Maselko et al. were the first to use ion-exchange resins for immobilization of ferroin and also reported the effect of the electric double layer caused by the remaining high charge density on the resin.’ In contrast to gel g, their gel systems possess negative charges (see Table I), which concentrate H+ and repel negatively charged species. In addition to these ion-exchange resins-cation and anion exchangers-a third discrete-gel system is available. Gel f (Fe(batho),/silica gel) is regarded to be neutral and hence we can examine the real “size effect” of discrete gel systems apart from the effect of electrical interaction. A clear example is that gel f was different from continuous silica gel (c) in its dependence on the concentration of the reacting media. When gel f was put in contact with the standard solution, there appeared a fine, complex structure with a wavelength of 0.6 mm (Figure 7A). At slightly different concentrations the contrast of the structures became somewhat better (Figure 7B). In a half-diluted standard solution, however, gel f showed a clear pattern of a wavelength of ca. 2 mm (Figure 7C) which equals the normal pattern obtained in continuous silica gel (c) in the standard solution (Figure 7D). This means that discrete gel systems respond to the aqueous reacting media more sensitively than continuous ones because of the large total surface area of gel particles. This size effect may be even more pronounced in case of ion-exchange resins because the catalysts are immobilized only on the surface of the resins. Outlook In this paper new ferroin-type catalysts, Fe(batho), and Fe[batho(S03)J3, are dealth with. The experimental results in the present gel systems indicate that there is no significant difference in pattern formation between these two catalysts and ferroin. But
Gel Systems for the BZ Reaction
The Jotlrrnal of Physical Chemistry, Vol. 95, No. 15, 1991 5837
A
C
B
D
Figure 7. BZ patterns observed in thin layers of discrete (A-C) and continuous (D) silica gels (gels f and c, respectively). Initial concentrations: (A) standard reacting solution, (B) [H2S04]= [NaBr03] = 0.28 M, [malonic acid] = 0.56 M, (C) half-diluted standard reacting solution, and (D) standard reacting solution.
in general, as the standard redox potential of ferroin-type catalysts depends on their complexing their behavior, the oscillation periods for example, may be different. The velocity of plane BZ waves in gel systems is equal to that of aqueous fluid systems even when the catalyst is immobilized. According to theory,*O however, the dependence of the velocity on the curvatureof a wave front is no more linear when the catalyst is immobilized. This is to be examined further in gel systems. As an interesting feature the intrinsic microinhomogeneities in discrete systems occasionally result in spontaneous formation of multiarmed spirals as mentioned above. In addition, discrete systems provide novel possibilities to control the reaction by the size effect and the electrical effect resulting from surface charge density. Comparison of pattern formation by use of positively charged, negatively charged, and neutral discrete systems is one of the interesting, newly arising problems. The mechanical stiffness and the openness of the catalyst-
immobilized gel systems enables us to apply arbitrary boundary conditions to excitable media of any shape-plane, membranous, cylindrical, spherical, and so on. A variety of new findings may be obtained from such experiments on chemical patterns purely coupled with diffusion, and they provide great support for theoretical frameworks. The essence of the present work is condensed in Table I. Although there still remains ample space for novel gel systems to enter into it, Table I will be a good help for choosing a suitable gel system for certain experiments. Acknowledgment. T.Y. thanks N E D 0 (the New Energy and Industrial Technology Development Organization, Japan) for support to stay at the Max-Planck-Institut. Helpful discussions with J. Ungvarai and the technical assistance of C. Riemer are gratefully acknowledged. This work was supported by the Stiftung Volkswagenwerk, Hannover.
