Turing Pattern Formation by the CIMA Reaction in a Chemical System

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Turing Pattern Formation by the CIMA Reaction in a Chemical System Consisting of Quaternary Alkyl Ammonium Cationic Groups Kouichi Asakura,*,† Ryo Konishi,† Tomomi Nakatani,† Takaya Nakano,† and Masazumi Kamata‡ † ‡

Department of Applied Chemistry, Faculty of Science and Technology, Keio University, Yokohama 223-8522, Japan Department of Beauty and Arts, Yamano College of Aesthetics, Hachioji 192-0396, Japan ABSTRACT: For the spontaneous generation of a Turing pattern, two intermediate species, an activator and an inhibitor, should be generated with the diffusion coefficient of the activator smaller than that of the inhibitor. The chlorite
iodide
malonic acid (CIMA) reaction that generates the activator, I
, and inhibitor, ClO2
, was performed in an open gel reactor. In order to lower the effective diffusivity of I
, micelles of quaternary alkyl ammonium cationic amphiphiles and polymers having a quaternary alkyl ammonium cationic side chain were combined in the CIMA reaction system in an open gel reactor. A Turing pattern formation was observed with the addition of n-dodecyltrimethylammonium bromide. Employing the gel reactor prepared by the polymerization of a monomer having quaternary alkyl ammonium cationic side chains also leads to the generation of a Turing pattern. The micelles and polymers are believed to trap I
in their vicinity as a counterion to lower the effective diffusivity.

’ INTRODUCTION Stationary concentration patterns are ubiquitous in nature. Typical examples include periodic concentration patterns of pigments on the body surface of animals such as angelfish, zebras, and tigers. In 1952, Alan Turing proposed a theoretical model for the spontaneous formation of stationary concentration patterns in a reaction-diffusion system.1 Spatially periodic stationary concentration patterns generated by following the Turing model are called a Turing pattern. It has been one of the central subjects of dissipative structure, i.e., self-organization in far-from-equilibrium systems.2
5 For the formation of a Turing pattern, two intermediate species, an activator and an inhibitor, are generated with the diffusion coefficient of the activator smaller than that of the inhibitor. The first experimental evidence of a Turing pattern was achieved in 1990 in the chlorite
iodide
malonic acid (CIMA) reaction in an open gel reactor in the presence of starch.6 Conditions after the initial induction period of the CIMA reaction were the same as the initial conditions of the chlorine dioxide
iodine
malonic acid (CDIMA) reaction. The activator, I
, and the inhibitor, ClO2
, were generated as the intermediates of the reaction.7
10 In this case, the activator, I
, forms a complex with starch to lower its effective diffusivity relative to that of the inhibitor, ClO2
.7
10 Addition of polyvinyl alcohol instead of starch11 and utilizing gels with a high concentration of a crosslinking agent as a reaction medium12 also lowered the effective diffusivity of I
to form a Turing pattern. Another example of a Turing pattern formation was observed in the Belouzov
Zhabotinsky (BZ) reaction in a water-in-oil Aerosol OT (AOT) microemulsion system.13 In this case, the higher solubility of Br2 in the continuous oil phase of the microemulsion makes the effective diffusion coefficient of the inhibitor, Br
, much larger than that of r 2011 American Chemical Society

the activator, HBrO2, to satisfy the conditions in which a Turing pattern is generated. Recently, the generation of stationary pH patterns by Turing instability was found in thiourea
iodate
sulfite reaction in a gel oneside-fed unstirred tank reactor.14 In this study, we focused our attention on the high affinity of a quaternary alkyl ammonium cation for I
. High selectivity of N, N,N0 ,N0 -tetramethyl-N,N0 -dioctadecylethylene-1,2-diamine as a ligand of the ion-selective electrode for I
was reported.15 In addition, high counterion selectivity of the dodecyltrimethylammonium cation toward I
was determined by ion flotation.16,17 In aqueous media, long chain quaternary alkyl ammonium cationic surfactants form micelles. The effective diffusivity of I
was expected to be reduced if the CIMA reaction system contained micelles of cationic surfactants having the property to select I
as the counteranion, since I
is trapped in the vicinity of the micelles. A hydrophilic polymer having a quaternary alkyl ammonium cationic side chain was also expected to reduce the effective diffusivity of I
. Attempts were made to generate a Turing pattern by the CIMA reaction by adding the quaternary alkyl ammonium cationic surfactant, n-dodecyltrimethylammonium bromide (DTAB). An open gel reactor prepared by the polymerization of acrylamide (AM) with the cross-liking reagent N,N0 methylene bis-acrylamide (BAM) was used. A CIMA reaction without the addition of DTAB was also performed in an open gel reactor composed of a polymer having quaternary alkyl ammonium cationic side chains. In this case, the gels were prepared by the copolymerization of N,N-dimethylaminoethylacrylate methyl chloride quaternary salt (DMAEA-Q) and AM with BAM. Received: December 6, 2010 Revised: February 2, 2011 Published: March 18, 2011 3959

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Figure 1. Experimental setup for the open gel reactor. The gel plate along with a spacer was tucked between a pair of plastic boards having a circular hole with a diameter of 1.5 cm. This apparatus was then tucked between a pair of spacers and plastic boards having no holes. The whole system was clipped together, and the reservoir solutions were flowed continuously into the the space between the plastic board having circular hole and the one having no hole, to diffuse the chemical reagents into the open gel reactor. Reservoir A contained MA, KI, and H2SO4, and reservoir B contained KI, NaClO2, and DTAB. The flow rate of both reservoir solutions was 0.5 mL min
1, and they were flooded from the top of the spacer to keep the concentrations of all chemical reagents in the reservoir solutions constant. The volume of each reservoir solution box was 7.5 mL, indicating that the residence time was 15 min. The temperature of the whole system was kept at 25 °C.

’ EXPERIMENTAL SECTION Materials. N,N-Dimethylaminoethylacrylate methyl chloride quaternary salt (DMAEA-Q) was supplied by Kohjin Co., Ltd. nDodecyltrimethylammonium bromide (DTAB) was purchased from Tokyo Chemical Industry Co., Ltd. Acrylamide (AM), N, N0 -methylene bis-acrylamide (BAM), and N,N,N0 ,N0 -tetramethylethylenediamine were purchased from Wako Pure Chemical Industries, Ltd. H2SO4, KI, and NaClO2 were purchased from Kanto Chemical Co., Inc. Ammonium persulfate was purchased from MP Biomedicals, LLC. Malonic acid (MA) and triethanolamine were purchased from Sigma-Aldrich Corporation. Preparation of Polymer Gel Plates. The gel plate for the CIMA reaction was prepared by the polymerization of AM with the crosslinking reagent, BAM, in a mold. An aqueous solution (18 mL) containing 0.18 g of AM and 0.048 g of BAM was mixed with 30 μL of N,N,N0 ,N0 -tetramethylethylenediamine and 80 μL of 9.1 wt % aqueous solution of ammonium persulfate. The solution was poured into a mold having a thickness of 3 mm, and the polymerization took place for 1 h at 25 °C. The gel plate composed of the polymer having quaternary alkyl ammonium cationic side chains was prepared by the copolymerization of DMAEA-Q and AM with BAM. An aqueous solution (20 mL) containing 3.00 g of DMAEA-Q, 0.20 g of AM, and 0.16 g of BAM was mixed with 80 μL of 30 wt % aqueous solution of triethanolamine and 80 μL of 20 wt % aqueous solution of ammonium persulfate. A mold having a thickness of 1.5 mm was used, and the polymerization took place for 5 h at 60 °C. Both PAM and P(DMAEA-Q
AM) gel plates were picked up from the mold and washed with water for 1 day. During the washing process, the P(DMAEA-Q
AM) gel plate was swelled to a thickness of ∼3 mm, while the PAM gel scarcely swelled. Both polymer gel plates thus had almost the same thickness when they were used for the open gel reactor for the CIMA reaction. CIMA Reaction in an Open Gel Reactor. The open gel reactor was assembled by putting the gel plate into two reservoir solution boxes, as shown in Figure 1. The CIMA reaction was performed by flowing two reservoir solutions through the boxes

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to make the chemical reagents diffuse in the open gel reactor. Flow of the reservoir solutions was continued for 2 h at 25 °C. The formation of the Turing pattern in the gel reactor was confirmed by the observation by USB microscope (M2, Scalar Corporation). Under some experimental conditions, very clear patterns were generated and the confirmation of the pattern formation was possible by the observation by the naked eye. The observation was accomplished by stopping the flow of the reservoir solutions, immediate removal of the gel plate, and observation using an optical microscope (BX51, Olympus Corporation), since the images observed by optical microscope were much clearer than the ones observed by USB microscope. Determination of Spatial Periodicity of the Turing Pattern. The spatial periodicity of the concentration patterns generated in the open gel reactors was analyzed by two-dimensional spatial Fourier transform by ImageJ developed in National Institute of Mental Health, Bethesda, Maryland, USA, and available on the Internet. Power spectra of the optical microscope images and their histograms were obtained.

’ RESULTS AND DISCUSSION Turing Pattern Formation by the CIMA Reaction in the Presence of Quaternary Alkyl Ammonium Cationic Surfactant. The PAM gel reactor was used, and experiments were carried

out by varying the concentrations of MA and H2SO4 in the solution of reservoir A. Concentrations of other reagents were fixed at [KI] = 2.0  10
3 M in reservoir A and [KI] = 2.0  10
3 M, [NaClO2] = 1.9  10
2 M, and [DTAB] = 4.0  10
2 M in reservoir B. The formation of several types of Turing patterns, such as stripe, labyrinth, hexagonal, rhombic, and black eye, in quasitwo-dimensional reaction-diffusion systems has been reported.18 In this experiment, two types of Turing patterns, hexagonal and diffuse (Figure 2a and b), were generated in the PAM gel reactor. Dark orange network structures were generated in each case, indicating that concentration patterns of I3
arose spontaneously. Like the other examples of Turing pattern formation in the open gel reactor,6,9 patterns thus generated were essentially two-dimensional. A concentration gradient of reactants from the boundary is formed in the open gel reactor to limit the range at which Turing instability is generated.9 Relatively small concentration ranges in [MA] and [H2SO4] in which a Turing pattern was generated were found, as shown in the phase diagram in the [MA]
[H2SO4] plane (Figure 3a). All patterns observed were classified as diffuse patterns except for one generated when [MA] = 3.9  10
3 M and [H2SO4] = 3.0  10
2 M. In order to see the global behavior of the Turing pattern formation, the next experiment was carried out by fixing the concentrations of MA and H2SO4 in the solution of reservoir A at the prior values, i.e., [MA] = 3.9  10
3 M and [H2SO4] = 3.0  10
2 M, and changing the concentrations of KI and NaClO2 in the solution of reservoir B. The concentrations of other reagents were [KI] = 2.0  10
3 M in reservoir A and [DTAB] = 4.0  10
2 M in reservoir B. A Turing pattern was observed in relatively large concentration regions of the phase diagram in the [KI]
[NaClO2] plane (Figure 3b). Not only hexagonal and diffuse patterns were observed but also a black eye pattern (Figure 2c). In all experiments, the concentration of DTAB in the solution of reservoir B was 4.0  10
2 M. The concentration gradient of DTAB was assumed to be formed in the open gel reactor, since DTAB was not contained in the solution of reservoir A. The critical micelle concentration of DTAB and its corresponding 3960

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Figure 2. Patterns observed in an open PAM gel reactor by CIMA reaction in the presence of DTAB. (a) Hexagonal pattern. Reservoir A: [MA] = 3.9  10
3 M, [KI] = 2.0  10
3 M, and [H2SO4] = 3.0  10
2 M. Reservoir B: [KI] = 2.0  10
3 M, [NaClO2] = 1.9  10
2 M, and [DTAB] = 4.0  10
2 M. (b) Diffuse pattern. Reservoir A: [MA] = 3.9  10
3 M, [KI] = 2.0  10
3 M, and [H2SO4] = 3.0  10
2 M. Reservoir B: [KI] = 1.6  10
3 M, [NaClO2] = 1.0  10
2 M, and [DTAB] = 4.0  10
2 M. (c) Black eye pattern. Reservoir A: [MA] = 3.9  10
3 M, [KI] = 2.0  10
3 M, and [H2SO4] = 3.0  10
2 M. Reservoir B: [KI] = 1.6  10
3 M, [NaClO2] = 1.5  10
2 M, and [DTAB] = 4.0  10
2 M.

Figure 3. Overview of Turing pattern formation by the CIMA reaction in the open PAM gel reactor in the presence of a quaternary alkyl ammonium cationic surfactant: (a) phase diagram in the [MA]
[H2SO4] plane; (b) phase diagram in the [KI]
[NaClO2] plane.

Figure 4. Two-dimensional spatial Fourier transform of optical microscope images. Power spectra and their histograms of the (a) hexagonal pattern shown in Figure 2a, (b) diffuse pattern shown in Figure 2b, and (c) black eye pattern shown in Figure 2c. The abscissa and ordinate of the histogram are radius (/pixels) and normalized integrated intensity, respectively.

iodide salt, DTAI, is (1.4
1.6)  10
2 M19 and 7.1  10
3 M,20 respectively, which are much smaller than the concentration of DTAB in the solution of reservoir B. Micelles of n-dodecyltrimethylammonium anion are thus expected to be formed in at least two-thirds of the open gel reactor based on the exposed surface attached to the solution of reservoir B. Control experiments were

carried out without adding DTAB in the solution of reservoir B. No Turing pattern was observed in the control experiments. Micelle formation of n-dodecyltrimethylammonium cationic amphiphiles to reduce the effective diffusivity of I
is therefore essential for Turing pattern formation. The mechanism for the generation of Turing instability in this reaction system is different 3961

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The Journal of Physical Chemistry B from the one in the BZ reaction in a water-in-oil AOT microemulsion system. In the BZ
AOT system, it was not the surfactant itself but the continuous oil phase of microemulsion that lowered the effective diffusivity of the activator.13 The spatial periodicity of the three patterns shown in Figure 2 was analyzed by two-dimensional spatial Fourier transform by ImageJ. Power spectra and their histograms were obtained, as shown in Figure 4. Hexagonal character was observed in the power spectrum shown in Figure 4a. In this case, the characteristic length of spatial periodicity was determined to be 0.35 mm. In the case of the diffuse pattern shown in Figure 2b, the characteristic length was not clearly determined (Figure 4b). The black eye pattern shown in Figure 2c does not have a strict regular hexagonal symmetry, and therefore, no hexagonal character was observed in the power spectrum shown in Figure 4c. Since a perfect black eye pattern was not generated in the optical microscope image, the characteristic length was not clearly determined by the histogram. Turing Pattern Formation by the CIMA Reaction in a Polymer Gel Containing Quaternary Alkyl Ammonium Cation Side Chain. Attempts were made to generate Turing patterns in the P(DMAEA-Q
AM) gel reactor. Since the open gel reactor itself contains quaternary alkyl ammonium cationic groups, DTAB was not added in the reservoir solution. The experiment was carried out by changing the concentrations of KI and NaClO2 in the solution of reservoir B. Concentrations of other reagents were [MA] = 4.0  10
3 M, [KI] = 1.3  10
3 M,

Figure 5. Picture of the patterns observed in the open P(DMAEAQ
AM) gel reactor by the CIMA reaction in the absence of DTAB taken by a regular digital camera. Reservoir A: [MA] = 4.0  10
3 M, [KI] = 1.3  10
3 M, and [H2SO4] = 7.5  10
3 M. Reservoir B: [KI] = 3.2  10
4 M and [NaClO2] = 1.9  10
2 M.

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and [H2SO4] = 3.0  10
2 M in reservoir A, and no reagent other than KI and NaClO2 were added to reservoir B. The color contrast of the patterns generated in the P(DMAEA-Q
AM) gel reactor in the absence of DTAB was clearer than the ones generated in the experiments utilizing the PAM gel reactor in the presence of DTAB. In some cases, taking a clear picture of the pattern by regular digital camera was possible, as shown in Figure 5. As in the case of the patterns generated in the PAM gel reactor in the presence of DTAB, the color of the structures was dark orange, indicating that the concentration patterns of I3
also arose spontaneously in this chemical system. Quaternary alkyl ammonium side chains of P(DMAEA-Q
AM) may form traps for the activator of the CIMA reaction, I
, to reduce its effective diffusivity to satisfy the condition for the Turing instability. Two types of Turing patterns, hexagonal and labyrinth (Figure 6a and b), were generated in extensively large concentration regions of the phase diagram in the [KI]
[NaClO2] plane, as shown in Figure 7. The P(DMAEA-Q
AM) gel reactor, however, was collapsed when [KI] was relatively high and [NaClO2] was relatively low. In some cases, both patterns were generated simultaneously, as shown in Figure 6c. The power spectrum obtained by two-dimensional spatial Fourier transform of the pattern shown in Figure 6a clearly exhibited hexagonal character, as

Figure 7. Overview of Turing pattern formation by the CIMA reaction in the open P(DMAEA-Q
AM) gel reactor in the absence of DTAB. Phase diagram in the [KI]
[NaClO2] plane.

Figure 6. Patterns observed in the open P(DMAEA-Q
AM) gel reactor by the CIMA reaction in the absence of DTAB. (a) Hexagonal pattern. Reservoir A: [MA] = 4.0  10
3 M, [KI] = 1.3  10
3 M, and [H2SO4] = 7.5  10
3 M. Reservoir B: [KI] = 2.6  10
3 M and [NaClO2] = 9.6  10
3 M. (b) Labyrinth pattern. Reservoir A: [MA] = 4.0  10
3 M, [KI] = 1.3  10
3 M, and [H2SO4] = 7.5  10
3 M. Reservoir B: [KI] = 2.6  10
3 M and [NaClO2] = 1.9  10
2 M. (c) Coexistence of the hexagonal and labyrinth patterns. Reservoir A: [MA] = 4.0  10
3 M, [KI] = 1.3  10
3 M, and [H2SO4] = 7.5  10
3 M. Reservoir B: [KI] = 3.2  10
3 M and [NaClO2] = 1.9  10
2 M. 3962

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’ REFERENCES

Figure 8. Two-dimensional spatial Fourier transform of optical microscope images. Power spectra and their histograms of the (a) hexagonal pattern shown in Figure 5a and the (b) labyrinth pattern shown in Figure 5b. The abscissa and ordinate of the histogram are radius (/pixels) and normalized integrated intensity, respectively.

shown in Figure 8a. Since the color contrast of the patterns was clear, the spatial periodicity was accurately analyzed by ImageJ. Characteristic lengths of spatial periodicity of both hexagonal and labyrinth patterns were determined to be 0.26 mm. They were therefore shorter than the ones generated in the PAM gel reactor in the presence of DTAB.

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’ CONCLUSION In the present study, we focused our attention on the high affinity of a quaternary alkyl ammonium cation with I
. The CIMA reaction that generates I
as the activator was carried out in a chemical system consisting of quaternary alkyl ammonium cationic groups. Micelles of quaternary alkyl ammonium cationic amphiphiles and polymers having quaternary alkyl ammonium cationic side chains were applied. Turing pattern generation was observed in both cases. The micelles and polymers are believed to trap I
in their vicinity as a counterion to lower the effective diffusivity to satisfy the conditions for the Turing instability. ’ AUTHOR INFORMATION Corresponding Author

*Address: Department of Applied Chemistry, Faculty of Science and Technology, Keio University, 3-14-1, Hiyoshi, Kohoku, Yokohama 223-8522, Japan. Phone: þ81-45-566-1553. Fax: þ81-45-566-1560. E-mail: [email protected].

’ ACKNOWLEDGMENT We thank Keio University Center for Research Promotion’s Grant Programs for Researchers. We also thank Dr. Daniel P. Predecki for his useful discussions. 3963

dx.doi.org/10.1021/jp111584u |J. Phys. Chem. B 2011, 115, 3959–3963