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Feb 15, 2017 - Self-organization (SO) of dissipative patterns in reaction-diffusion systems far from equilibrium(3, 4) is a separate relatively new br...
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Self-Organization Induced by Self-Assembly in Microheterogeneous Reaction-Diffusion System Alexander A. Cherkashin‡ and Vladimir K. Vanag*,† †

Centre for Nonlinear Chemistry, Immanuel Kant Baltic Federal University, 14 A. Nevskogo str., Kaliningrad 236016, Russia Department of Biophysics, Faculty of Biology, Lomonosov Moscow State University, Moscow 119899, Russia

‡

S Supporting Information *

ABSTRACT: When acrylamide (AA) monomers are added to the Belousov−Zhabotinsky (BZ) reaction incorporated into nanodroplets of water-in-oil aerosol OT (AOT) microemulsion (the BZ-AOT system), free radicals produced in the BZ reaction initiate polymerization of AA monomers and polyacrylamide particles are formed. These particles change the microstructure of the AOT microemulsion thus inducing the transition from Turing patterns to new dissipative patterns which can be either stationary “black” spots or waves.

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INTRODUCTION Self-assembly (SA), for example, a formation of thermodynamically stable micelles in a mixture of two immiscible liquids (water and oil) with the aid of surfactants1 or a formation of solid (metal) nanoparticles,2 is a well-known field of science. Self-organization (SO) of dissipative patterns in reactiondiffusion systems far from equilibrium3,4 is a separate relatively new branch of science (sometimes called “nonlinear chemistry”). One of the most famous examples of dissipative patterns is chemical waves in the Belousov−Zhabotinsky (BZ) reaction.5 The BZ reaction6,7 is the bromination and oxidation of organic substrates, usually malonic acid, catalyzed by the metal ions (or metal ion complexes) in acidic medium. Ferroin [tris(1,10phenanthroline)iron(II)] and Ru(bipy)32+ [tris(2,2′-bipyridyl)ruthenium(II)] are widely used as the catalysts. About 15 years ago, it was shown that a combination of selfassembled nanodroplets in the water-in-oil aerosol OT microemulsion with the BZ reaction inside (BZ-AOT system) gave rise to a zoo of new dissipative patterns including Turing pattern,8 antiwaves,9 segmented spirals,10 and many others.11 New patterns originate due to the difference in the diffusion coefficients of the reactive species (inhibitors and activators) in the structured media. An assumption of the dynamical interaction between SA and SO has been realized only recently. In a 2D array of the hexagonally packed BZ-microdroplets fabricated in a microfluidic device by mixing oil and the aqueous BZ reactive solution,12 stationary Turing patterns can occur first and then the BZ microdroplets in the reduced (oxidized) state become larger (smaller) in size.13 That is the first observation of a transformation of stationary dissipative patterns into thermodynamically stable patterns predicted by Turing.14 Dissipative © 2017 American Chemical Society

patterns in the form of the BZ waves can also change a shape of pieces of the Yosida-gel.15,16 Interplay between SA and SO with positive and negative feedbacks is widely used by living systems.17 Our approach is inspired by living matter and its fascinating feature of compartmentalization. Herein we demonstrate for the first time how dissipative patterns in the BZ-AOT system initiate first a formation of polymer nanoparticles (nanogel) (SA-II) in nanodroplets of AOT-microemulsion (SA-I). Then newly formed microstructures change dissipative patterns of the BZ-AOT system (SO-I, patterns before polymerization, transform into SO-II, new patterns induced by polymerization). In other words, we deal with the feedback loops between SA and SO processes that can be schematically expressed as a chain of the following events: SA-I → SO-I → SA-II → SO-II. The effect of the homogeneous BZ reaction in the aqueous phase on the polymerization of acrylonitrile was first demonstrated by Váradi and Beck18 and then reproduced and carefully studied in the Pojman group.19 Here we use the other monomers: acrylamide (AA) with bis-acrylamide (bis-AA) (a bifunctional cross-linker), a mixture which is widely used for preparation of the polyacrylamide (PAA) gel.20 Searching for suitable gels, the PAA gel was found to be a convenient tool to study trigger waves in the BZ reaction.21 Two methods are usually used to generate free radicals for radical polymerization of a mixture of AA with bis-AA: (i) chemical method, where a mixture of ammonium persulfate and TEMED (N,N,N′,N′Received: December 1, 2016 Revised: February 15, 2017 Published: February 15, 2017 2127

DOI: 10.1021/acs.jpcb.6b12089 J. Phys. Chem. B 2017, 121, 2127−2131

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AOT system. We explore poly(ethylene glycol) (PEG) diamine with the molecular weight equal to 2000. Even relatively small concentrations of PEG-(NH2)2 added induce the transition from the labyrinthine to hexagonal (spot) Turing patterns (see Figure 1). This transition happens at different droplet fractions

tetramethylethylenediamine) is used, and (ii) photochemical method in which riboflavin and light are employed.

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EXPERIMENTAL SECTION The AOT microemulsion is characterized by the two parameters: ω = [H2O]/[AOT] and the volume droplet fraction ϕd.11 Parameter ω determines the radius R of nanodroplets as R/nm = 0.17ω.11 Two stock microemulsions with the same molar ratio ω and volume droplet fraction ϕd were prepared by mixing 1.5 M AOT in octane with the aqueous solutions of malonic acid and H2SO4 (MEI) or with NaBrO3 and a catalyst (MEII) (catalyst is Ru(bpy)32+ or ferroin). Equal quantities of PEG diamine or acrylamide (with bis-acrylamide) were introduced into MEI and MEII to obtain the desired concentrations of polymer or monomer. Reactive ME was obtained by mixing equal volumes of MEI and MEII. Octane was added to this mixture to obtain the desired ϕd. Electrical conductivity of microemulsions was measured with YSI 3200 conductivity meter. Size distribution of water nanodroplets and polymer particles was measured by dynamic light scattering with DynaPro NanoStar, Wyatt Technology. A small volume (ca. 0.1 mL) of reactive ME was sandwiched between two flat glass windows separated by a Teflon gasket (Zefluor membrane, 80 μm in thickness). The edges of the glass windows were sealed with a Teflon tape and then the two windows were tightly pressed together in a holder to form a closed reactor. Patterns were observed through a Zeiss Stemi 2000-C stereo microscope in the transmitted light passed through one of the interference filters with the following wavelength maxima of the narrow transmitted band: 510 nm (in the case of ferroin as a catalyst) or 450 nm [in the case of Ru(bpy)3]. The microscope was equipped with a QICAM 12bit CCD camera connected to a computer. The wavelength of patterns was determined from the maximum of its spatial Fourier transform.

Figure 1. Turing patterns in the BZ-AOT microemulsion at ω = 15.2, ϕd = 0.35, [MA] = 0.25 M, [H2SO4] = 0.2 M, [NaBrO3] = 0.18 M, [ferroin] = 4.15 mM, and [PEG diamine] = (a) 0, (b) 10 mM. The Turing wavelength λT/mm = (a) 0.225, (b) 0.20; image size (mm × mm) = (a), (b) 3.7 × 3.7. The spatial Fourier transform of the Turing patterns are in the left bottom corners.

ϕd, when the BZ-AOT system is far from (as in Figure 1) or close to the percolation transition (Figure S1 in Supporting Information). On the other hand, it is known that polymerization of water-soluble monomers (for example, AA) can happen in water-in-oil microemulsions, for example, in the AOT microemulsion.26 Therefore, we expect that the polymerization of AA induced by primary patterns in the BZ-AOT system (SO-I) should also lead to the formation of new dissipative patterns. We will call the BZ-AA system incorporated into the AOT microemulsion a BZ-AA-AOT system. Typical patterns found in the BZ-AA-AOT system due to the BZ-induced polymerization of AA monomers are shown in Figure 2. For 0 ≤ [AA] < 2 mM, the labyrinthine Turing patterns occur with either continuous black (see Figure 2a) or white [Figure S2 in Supporting Information (SI)] background. In the range 2 mM < [AA] < 50 mM, new dissipative patterns emerge: the randomly distributed stationary black spots with no spatial periodicity (see Figure 2b and c). When they emerge (Figure 2b, which corresponds to 900 s in Figure 2d), they are surrounded by bright annular halos (see Movie S1 in SI). Note that the black spots are darker than the gray background, while white halos are lighter, i.e., we observe three distinct levels of the redox states of the catalyst. After the emergence, the black spots shrink slightly, but then start growing in size (see the time interval between 900 and 1100 s in the space-time plot in Figure 2d). The white waves emerge 1500−1600 s after the beginning of the experiment. Typical white waves are shown in Figure 2c and in Movie S2 (in SI). These waves cannot enter the areas occupied by the black spots; they go round or even rotate around some black spots. White periodical horizontal segments in Figure 2d represent the propagation of white waves across the black segment shown in Figure 2c. During wave propagation, some black spots disappear, while others can grow and merge reaching approximately 1 mm in diameter in 1 h (see Figure S3 in SI). Note that these black spots, which are the islands of high concentration of the reduced state of the catalyst, are similar to the black spots found earlier.27 The model developed in that

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RESULTS AND DISCUSSION Since the BZ reaction itself is a good source of free radicals, we have first tested the idea that the BZ reaction can initiate polymerization of acrylamide monomers. In all our experiments on the BZ-induced polymerization of acrylamide monomers, we used a mixture of AA and bis-AA with the molar ratio [AA]/ [bis-AA] = 168. We will call this system a BZ-AA system. In the case of the BZ-AA system catalyzed by the light sensitive catalyst Ru(bpy)3, illumination resulted in the formation of a very strong PAA gel (at [AA] > 2 M). In the case of ferroin as a catalyst, a single trigger BZ wave resulted in the same outcome, the PAA gel (at [AA] > 2 M). This frontal polymerization is similar to recently found formation of thiol−acrylate hydrogel induced by the front propagation in the enzymatic autocatalytic reaction.22 So, to produce the AA gel, we do not need both methods (i) and (ii) mentioned in the Introduction Section. If however [AA] is small enough, polymerization leads to the formation of small polymer particles rather than a continues gel.23 Addition of small polymer particles (like poly(ethylene oxide), for example) changes significantly dissipative patterns in the BZ-AOT system affecting the characteristic wavelengths of the dash waves24 or shortening the characteristic wavelength of labyrinthine Turing patterns.25 These effects are due to the formation of droplet clusters induced by polymers. We also tested the effect of polymers on Turing patterns in the BZ2128

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dynamic light scattering (DLS) and electrical conductivity measurement of the BZ-AA-AOT system. First, we made sure that the PAA particles could be obtained in the aqueous phase at the concentrations of [AA] used in our experiments. We varied [AA] in a broad range (from a few mM up to several M) keeping the ratio [AA]/[bis-AA] constant. We used two methods for polymerization: (1) “persulfate ammonium with TEMED” and (2) “BZ reaction”. Gel was formed at [AA] > 1 M in both methods of polymerization. At smaller [AA], the reactive mixture remains in a liquid state and the DLS method reveals several peaks in a broad range of sizes (see Figure 3a,c)

Figure 2. Patterns in the BZ-AA-AOT system at different [AA] = (a) 2 mM (labyrinth), (b) and (c) 21 mM (black spots), and (e) 4.2 M (latex); ϕd = (a)−(c) 0.45, (e) 0.5; ω = (a)−(c) 10, (e) 15.2. The initial concentrations are (a)−(c) [NaBrO3] = 0.25 M, [MA] = 0.1 M, [H2SO4] = 0.3 M, [Ru(bpy)3] = 4 mM; (e) [NaBrO3] = 0.18 M, [MA] = 0.25 M, [H2SO4] = 0.2 M, [ferroin] = 4 mM. Frame size (mm × mm) = (a), (b) 5.9 × 4.4, (c) 3.6 × 4.4, (e) 3.55 × 3.1; scale bar in (e) equals 0.5 mm. The size of the space-time plot in (d) taken along the black bar in (c) is 1.13 mm × 3000 s. The period of the waves seen in (c) equals 62 s. The Turing wavelength λT of the labyrinthine patterns in (a) is equal to 0.44 mm. Snapshots (b) and (c) are taken 15 and 30 min, respectively, after the beginning of the experiment.

Figure 3. DLS spectra for the size distribution of the PAA particles in (a),(c) the aqueous phase and (b),(d) the BZ-AOT microemulsion with ω = 10 and ϕd = 0.45 at [AA]/mM = (a), (b) 50, (c), (d) 500; [MA] = 0.1 M, [H2SO4] = 0.3 M, [NaBrO3] = 0.25 M, [Ru(bpy)3] = 3.3 mM.

work for subcritical Turing instability describes the localized black spots that have three distinct redox states of the catalyst, or to be more exact, the almost entirely reduced state in the center of the black spot, the almost entirely oxidized state around the black spot (which corresponds to our white halos), and the intermediate redox state unstable to large perturbations (the steady state, which corresponds to the gray background). As soon as the localized black spots occupy the entire area, the gray background disappears and normal Turing patterns (like in Figure 1) with two distinct levels of gray (“black” and “white”) emerge. In the range of [AA] between 0.2 and 1 M, no patterns were observed. At still larger [AA] (2−5 M), blots of stable polymers or latex particles emerge (see Figure 2e). These particles are hardly resolved via our stereo microscope at [AA] = 2 M (Figure S4 in SI), but clearly seen at [AA] = 4.2 M with the average diameter of the particles equal to 39 μm (Figure 2e). The chaotic phase BZ waves can coexist with the latex particles at larger ω (= 15.2) and ϕd (= 0.5) (see Figure S5 in SI). The full list of experiments on the BZ-AA-AOT system at ω = 10, ϕd = 0.45, and at the constant concentrations of the initial BZ reactants ([MA] = 0.1 M, [H2SO4] = 0.3 M, [NaBrO3] = 0.25 M) is given in the Table S1 in SI. Note that an increase in the initial concentration of MA favors the emergence of the black spots, while an increase in the [H2SO4] or [NaBrO3] favors the emergence of waves at the same [AA], ω, and ϕd. The black spots shown in Figure 2b and c differ significantly from the white spots shown in Figure 1b. Therefore, we can suppose that the BZ-induced polymerization of AA monomers does not lead to small globular polymer particles incorporated into nanodroplets. To understand the nature of the patterns found, we have performed a series of the experiments on the

(this result is independent of the method of polymerization). At [AA] = 50 mM (or smaller), several separate peaks are observed (Figure 3a), while at larger [AA] (>0.1 M and around 0.5 M), all these peaks merge to a very broad peak spanning from 10 up to 100 nm (or even larger) (Figure 3c). A broad distribution of the sizes of the PAA nanogel particles at a relatively small [AA] was found elsewhere.23 In the BZ-AOT system with [AA] = 50 mM (or less), a broad distribution of peaks from 1 up to 1000 nm is also found by the DLS method (see Figure 3b). The left peak in Figure 3b is around 6−8 nm, which is very close to the diameter Dd of water nanodroplets (= 5−6 nm), while the maximum of the second peak, around 30 nm, is much larger than Dd. We can hypothesize that this peak (and probably the right peak as well) is due to the PAA particles formed in microemulsion. Note that the black spots shown in Figure 2b and c are found at [AA] < 50 mM. If however [AA] > 100 mM, the DLS spectra change dramatically (see Figure 3c,d). As in the case of the aqueous phase (Figure 3c), a very broad DLS peak emerges in the range of the diameters between 10 and 110 nm (Figure 3d). This peak shifts slightly to smaller values of the diameter if [AA] grows from 100 mM up to 4 M. This result suggests that large PAA particles or droplet clusters are formed at [AA] > 100 mM. Note that no dissipative patterns are observed at [AA] > 100 mM. Polydispersity of latex particles (nanogels) formed due to microemulsion polymerization of other monomers was found elsewhere.28 We have also measured the electrical conductivity of the BZAA-AOT microemulsion as a function of [AA] (see Figure 4). Figure 4 demonstrates that the increase in [AA] (starting at 2129

DOI: 10.1021/acs.jpcb.6b12089 J. Phys. Chem. B 2017, 121, 2127−2131

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The Journal of Physical Chemistry B ORCID

Vladimir K. Vanag: 0000-0002-9521-6650 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the “5-100” Program of the Immanuel Kant Baltic Federal University and by the RFBR grant No. 15-07-01726.

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Figure 4. Conductivity of the reactive BZ-AA-AOT microemulsion for different [AA] at ϕd = 0.45 and ω = 10. Concentrations: [MA] = 0.1 M, [H2SO4] = 0.3 M, [NaBrO3] = 0.25 M, [Ru(bpy)3] = 4 mM.

[AA] ≅ 100 mM) drastically elevates the conductivity, which indicates the percolation transition to the interconnected bicontinuous structure. It is known that no stationary dissipative patterns (like Turing patterns) are possible for this structural state of microemulsion,11 but waves can be observed. This increase in conductivity is especially pronounced at the vicinity of the percolation transition, when the droplet fraction ϕd of the BZ-AOT microemulsion is around 0.4−0.6.

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CONCLUSIONS Our finding of the cascade of SO and SA processes in the BZAA-AOT system opens a new avenue for creating both new dissipative and thermodynamically stable patterns that can be used for engineering of smart materials. We believe that similar processes take place in living systems during morphogenesis. For example, in some Charophytes algae, alternating pH bands with high and low pH (similar to Turing patterns) emerge on the surface of their intermodal cells under homogeneous illumination.29 Then calcification occurs only in the alkaline bands thus fixing the band patterns produced in the reactiondiffusion system. These final thermodynamically stable patterns remain even after the cell death. In some cases, the interplay between SO and SA creates feedbacks for switching between important regimes or states in biological systems, like in the case of bacterial self-organization.30 In our particular case of the BZ-AOT system, many other monomers and dynamical regimes of the system should be tested in future works including localized polymerization.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b12089. Turning patterns in the BZ-AOT system without and with PEG diamine; patterns observed in the BZ-AAAOT system: Turning patterns in the form of black labyrinth and white background, black spots in the BZAOT system with AA, no patterns in the BZ-AOT system at [AA] = 2.1 M, white latex particles and chaotic black waves (PDF) Movie of the emergence of black spots and bright annular halos corresponding to Figure 2b(AVI) Movie of the white waves and stationary black spots corresponding to Figure 2c (AVI)

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AUTHOR INFORMATION

Corresponding Author

*[email protected].

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