Sustained Large-Amplitude Chemomechanical Oscillations Induced

Article pubs.acs.org/JPCB

Sustained Large-Amplitude Chemomechanical Oscillations Induced by the Landolt Clock Reaction Judit Horváth* Centre de Recherche Paul Pascal, CNRS, 115 avenue Dr. A. Schweitzer, F-33600 Pessac, France Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112, Hungary S Supporting Information *

ABSTRACT: Synergetic chemomechanical oscillators represent a fundamentally new class of oscillators, where a clock reaction, owning no oscillatory chemical kinetics, generates shrinking−swelling cycles in a chemoresponsive gel under appropriate fixed nonequilibrium boundary conditions. Sufficiently large size-changes are a condition for continually switching between a reacted and an unreacted chemical state in the gel through sufficiently large differences in the diffusion time between the environment and the core of the gel. Two former experimental demonstrations with acid autocatalytic reactions were frustrated either by complex behaviors (chlorite−tetrathionate system) or by side reactions with the gel matrix (bromate−sulfite system). With the Landolt (iodate−sulfite) reaction, regular large-amplitude chemomechanical oscillations can be sustained for more than a week. This enabled a fine study of the temperature and stoichiometry range of operation. I have identified several key steps that are experimentally essential to the systematic design of further synergetic oscillators. The robust realization of this type of selforganization in artificial systems is currently unique.

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INTRODUCTION More than 60 years ago, when chemomechanical systems were first thought of, the main idea was to convert chemical ionization energy directly to mechanical work in an isothermal process using contractile, cross-linked polyelectrolyte gels.1 The biophysical analogy (muscle behavior) and the notion of work production in cycles had already been pointed out at that time. In the mid 1990s, autonomous chemomechanical oscillators were created by driving chemoresponsive gels by oscillatory chemical reactions.2,3 These reactions generated swelling− shrinking cycles, similar to heartbeats, without externally applied stimuli. The oscillatory reactions employed were either (1) pH oscillators (pH-responsive gels are easily available) that autonomously generated a periodically changing chemical environment around the gel4−7 or (2) the Belousov− Zhabotinsky (BZ) reaction where a metal ion complex, needed as a catalyst for this oscillatory reaction and undergoing periodic redox changes, was grafted to a polymer network, and therefore periodic chemical changes occured only inside the gel. The chemically induced periodic changes in charge number led to periodic swelling−shrinking of the network in a steady environment. The unique capacity of the BZ reaction to produce oscillatory redox changes over extended periods of time when closed up with a given amount of reactants (batch) gave rise to the construction of more and more sophisticated gadgets with different motile functions.8,9 Recently, our team has shown both theoretically and experimentally that a pH-clock reaction (e.g., an acidautoactivated reaction), with no oscillatory chemical kinetics © 2014 American Chemical Society

properties, can lead to oscillatory shrinking−swelling cycles in pH-responsive gels under appropriate constant boundary feed compositions.10−14 This is a fundamentally different class of chemomechanical oscillators that I shall refer to as synergetic chemomechanical oscillators. In this class, the size changes are not just a consequence of but also a condition for obtaining periodic dynamics. No chemical oscillation occurs without or with insufficient size changes in the gel. This opposes the above systems where the mechanical changes are merely tied to the reaction kinetics. Synergy between chemical processes and responsive elastic materials can give rise to phenomena that neither of the individual subsystems would exhibit under comparable conditions. A synergistic effect also underlies a system proposed to be a rhythmic drug-delivery automate where spontaneous periodic changes occur in the permeability of a gel membrane separating a permanently fed twocompartment system.15 At appropriate constant inputs, a pulsatile output is obtained. Synergetic effects are often evoked in biological morphogenesis or the development of rhythmic functions, where the elastic and interfacial properties of the tissues combine with the biochemical reactions and transport processes.16,17 In our approach, a piece of hydrogel is diffusively fed by reactants from a stationary, far-from-equilibrium chemical environment. The extent of reaction (or the approach to Received: May 23, 2014 Revised: June 19, 2014 Published: June 20, 2014 8891

dx.doi.org/10.1021/jp5050964 | J. Phys. Chem. B 2014, 118, 8891−8900

The Journal of Physical Chemistry B

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continuous stirred tank reactors (CSTR) or more recently in divided closed systems.34 Generally, to obtain oscillatory behavior in a system, the following conditions must be fulfilled: (1) The system must be far from thermodynamic equilibrium. In solution chemistry, this is ensured by operating the reaction in a CSTR. The ratio of the residence time of the CSTR (τCSTR) and the induction time of a simple autocatalytic reaction (τind) determines how far the system is from equilibrium. In the present case, the responsive gel is immersed in the stationary, low extent of reaction content of a CSTR. The reactants diffuse into the gel through the contact boundary while the products in the core of the gel diffuse out. The extent of reaction in the core of the gel grossly depends on the sum τCSTR + τdiff; τdiff is the time needed for the species to reach the core of the gel from the feed boundary by diffusion. (2) The system must involve a positive feedback mechanism. In our examples, this property is brought about by the pH-clock reaction itself that generates protons in an autoactivated cascade.25 In the chemomechanical experiments, conditions are set such that in the swollen state of the gel τCSTR < τind < (τCSTR + τdiff), so that in an initially swollen gel a pH drop occurs only in the gel. As a consequence, the appropriate pH-sensitive gel shrinks. (3) The system must contain a process that exerts negative feedback on the autoactivated process. In oscillatory mixed Landolt reactions, this is provided by a kinetic protonscavenging step, which is the oxidation of the second substrate by iodate.29−33 In a synergetic chemomechanical oscillator, with a simple pH-clock reaction, the reaction mechanism does not include such a scavenging step. The negative feedback is exerted through the decrease in τdiff associated with the shrinking of the gel. Then, to recover the low extent of reaction composition (pH ∼7) in the core of the gel, the gel should shrink so much that the overall residence time of reactants and products in the core becomes (τCSTR + τdiff) ≪ τind. Then the gel reswells. (4) Last, the positive feedback mechanism must evolve on a time scale shorter than the negative one. In the mixed Landolt reactions, this requires an appropriate hierarchy of the reaction rate constants. In chemomechanical systems, the autoactivatory chemical process must evolve faster than the shrinking of the gel. This is a standard situation in macroscopic polymer networks.

equilibrium composition) inside the gel depends sharply on the gel thickness in the case of clock reactions.18,19 It is low and nearly identical to that of the environment until a certain gel thickness is reached and abruptly becomes high when the characteristic time of exchange of reactants and products with the environment exceeds the induction time of the clock reaction. So swelling of the gel can switch on the domination of the autocatalytic process in the core of the gel (characterized by a high extent of reaction), while shrinking can turn off this dominance and can reestablish a low extent of reaction by the more rapid elimination of products and the replenishment of fresh reactants. To obtain a cyclic phenomenon, the gel should shrink in the reacted state in response to one of the products so that the size change exerts negative feedback on the extent of reaction in the gel. In oscillatory reactions, this negative feedback is of a chemical nature. Our former experimental investigations have shown that in this way physical (or geometrical) feedback can equivalently replace chemical feedback in an autonomous actuator, and kinetic oscillations are not absolutely needed to produce pulsating phenomena in responsive materials or tissues. Previously, two experimental examples had been assembled based on the above synergistic principle using two different pH-clock reactions and pHresponsive gels. However, the first system (based on the chlorite−tetrathionate, CT, superautocatalytic reaction) exhibited highly complex dynamical behaviors.13 Many of these are difficult to interpret in the absence of appropriate 3D theoretical developments.20 The second one (based on the bromate−sulfite, BS, reaction) was successfully described by a reliable kinetic and 1D polyelectrolyte swelling model,12 but the experimental demonstration was frustrated by a bromination side reaction which induced a gradual loss of the responsiveness of the gel and thus limited the working time to 1 to 2 days.14 Prolonged oscillatory lifetimes are essential to conducting refined studies on dynamical properties and on the limits of operation. The iodate−sulfite (IS) pH-clock reaction (Landolt reaction), chemically less aggressive than the BS reaction, is a more promising candidate in this respect. Furthermore, its spatial behavior in nonresponsive gels has been well explored both experimentally and theoretically.21−23

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THEORETICAL BASIS

The Landolt reaction, that is, the autocatalytic oxidation of hydrogen sulfite ions by iodate ions, is one of the oldest known isothermal, liquid-phase, nonlinear chemical reactions.24 It is a popular classroom demonstration of clock-reaction behavior as iodine appears abruptly after a well-defined induction time, τind, when the sulfite ions are nearly entirely consumed. The consumption of sulfite ions is associated with a sudden pH drop of about 4 units (from pH ∼7 to ∼3) as the solution loses its buffering capacity25 and a strong acid (sulfuric acid) is produced: IO3− + 3HSO3− → I− + 3SO4 2 − + 3H+

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MATERIALS AND METHODS Gel Synthesis. Monomers N-isopropylacrylamide (NIPA, Aldrich), N-tert butylacrylamide (NTBA, Acros), acrylic acid (AA, Fluka), and itaconic acid (IA, Acros) and cross-linker N,methylenebis(acrylamide) (MBA, Fluka, purum) were used as supplied. Free-radical polymerization was performed in 2:1 (v/ v) tert-butanol/water mixtures35 initiated by potassium persulfate (KPS, Prolabo, p.a.) and N,N,N′,N′-tetramethylethylenediamine (TEMED, Fluka, for electrophoresis). Chart 1 shows the comonomers per gel type. The pregel compositions are indicated in Table 1. The 2:1 mixture of methanol and water was also suitable for the synthesis and led to gels with equivalent equilibrium swelling characteristics. The use of other alcohols or sodium acrylate instead of acrylic acid led to phase separation during polymerization. For procedure details, see ref 14. The gels were removed by putting the molds in warm tap water (40−50 °C) and by pumping hot water from a plastic syringe through the

(R1)

Reaction R1 is autocatalytic for both protons and iodide ions.26,27 In the 1980s, several pH-oscillatory reactions were designed28 based on the Landolt reaction by adding a second reducing agent, such as ferrocyanide,29 thiourea,30,31 or thiosulfate.32,33 Their oxidation consumes protons and exerts negative feedback on the proton production step, R1. Oscillatory behavior is attained when these so-called twosubstrate Landolt or mixed Landolt reactions are operated in 8892



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(Carlo Erba, p.a.; 0.050 M), and (4) H2O. Solution (2) was kept under N2 and replaced with a fresh solution every 24 h. All solutions used Millipore water. To stabilize the pH in the CSTR, a high-molar-mass polymer with pH buffer capacity, the partial sodium salt of poly[acrylamide-co-(acrylic acid)], abbreviated as poly(AA/AAm), was fed at 1.6 g/L in the combined feed (Aldrich 511 471, acrylamide content = 81.7 wt %, Mw = 520 000, Mn = 150 000, residual monomer 0.310.21 At lower

2:1 (v/v) tert-butanol/water.

glass capillaries (⌀ 0.50 and 1.00 mm) or else by pulling out the collapsed gel with a pair of tweezers from the conical pipet tip molds. The gels were washed in ethanol−water mixtures (2:1, 1:1, and 1:2) for 3 h in each composition and stored in a 0.25 M ammonium acetate solution at pH 7 until use. Gel Characterization. Equilibrium swelling measurements were performed in Britton-Robinson buffer solutions. The concentration of acetic, phosphoric, and boric acids was 0.010 M each. NaOH solution was diluted from a 1 M standard with freshly boiled water. The Na+ concentration in the buffers was set to constant 0.050 M by NaCl. The diameter of the gel cylinders was determined as described in ref 14. Continuously Fed Reactor. The chemomechanical experiments were performed under controlled far-from-equilibrium conditions in a CSTR. For a detailed description of the CSTR and the experimental setup, see refs 13, 14, and 22. In all cases, the overall feed rate was 240 mL/h, corresponding to a residence time in the reactor of τCSTR = 45 mL/240 mL h−1 = 675 s. The reactants were fed by four precision piston pumps (Pharmacia P500) from four separated reservoirs, containing as follows (1) KIO3 (Sigma-Aldrich, puriss. p.a.; 0.060 M), (2) Na2SO3 (Sigma-Aldrich, puriss. p.a.; 0.180 M), (3) H2SO4 8893



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[KIO3]0/[Na2SO3]0 feed ratios between 0.270 and 0.310, a diffusion-driven instability termed long-range activation (LRA) developed, generating spatiotemporal oscillations even in the absence of oscillatory reaction kinetics or size changes.21−23 However, this LRA instability can develop only in neutral (or very weakly charged) gels because it requires that the activator (here the proton) diffuses much faster than the other main species. Numerical calculations revealed that the LRA instability ceases as soon as the ratio of the effective diffusion coefficients of the proton and the hydrogen sulfite ion falls from the natural 10 to 3.3.23 Immobile proton binding sites in the gel can considerably slow down the effective diffusion coefficient of protons through their reversible binding. In the abovementioned experiments, [−COOH]gel = 10 mM low-mobility carboxylate functional groups, added to the agarose gel as interpenetrating polyacrylate chains, completely quenched the LRA-generated oscillations in the IS reaction.22 For comparison, quenching in the CT reaction was obtained between [−COOH]gel = 10 and 15 mM monomolar concentration for these low-mobility carboxylate functions.19 The responsive gels used in the present study contain 87.5 mM carboxylate functional groups upon synthesis (Table 1). Even in the case of swelling to 200% in linear size, [−COOH]gel is still above the 10 mM concentration. Despite this fact, we have restricted the chemomechanical experiments to reaction mixtures with [KIO3]0/[Na2SO3]0 ratios of 0.320−0.340 where the LRA instability was not observed even in neutral gels. In order to elaborate on appropriate pH-responsive gels, first the pH range that separates the critical minimum F-state value from the maximum M-state value in the core of the gel should be known. However, the pH at the stability limits of the F and M states in the core of a gel (or the pH drop in the feed direction in the M state) can be estimated only indirectly, either from simulations or from the switching range of color pH indicators found to be appropriate for visualizing the position of acid fronts or waves in spatial dynamics studies. With the BS reaction, calculated concentration profiles in a gel with [−COOH]gel = 50 mM estimated the pH drop between pH 6.50 and 3.50.12 For comparison, the pH gaps between the two states in a CSTR in the absence of carboxylate groups were the same. Accordingly, chemomechanical oscillations were best realized with responsive gels having a swollen−shrunken transition between pH 6.50 and 4.50.14 With the IS reaction, concentration profiles were calculated only in neutral gels where the oscillatory LRA instability develops but not in charged gels in the spatial bistability region (i.e., at [KIO3]0/ [Na2SO3]0 > 0.310).23 The experimental usability of different color indicators (bromophenol blue and methyl orange) indicates that the pH gap between the F and M states in the IS reaction stretches over pH 4.50−3.00 or more.21,22 For comparison, in a CSTR the low extent of reaction F-state branch lies above pH 5.50 while the high extent of reaction steady T-state branch lies under pH 3.00.22 As shown in Figure 1a, the same values were obtained at the higher [KIO3]0/[Na2SO3]0 ratio chosen in this work (0.321 instead of 0.300) and at a somewhat longer residence time (τCSTR = 11.25 min instead of 7.1 min). As all indicated that the transition from the F to the M state occurs at lower pH in the IS-reaction than in the BS-reaction, we considered that pHresponsive gels with AA monomers (Chart 1a) should be more appropriate37 than the gels with MAA monomers used for the BS-chemomechanical oscillator.14 The pH range where the swelling−shrinking transition occurs can be adjusted within a

Figure 1. Buffering effect of a carboxylic acid feed on the bistability domain of the Landolt reaction in a CSTR as a function of sulfuric acid in the feed. Control parameters: τ = 11.25 min, ϑ = 30.0 °C. [KIO3]0 = 19.25 mM, [Na2SO3]0 = 60 mM, and [−COOH]0 denotes the average concentration of the carboxylate functional groups of macromolecular pH buffer poly(acrylamide-co-acrylic acid) in the solution. Δ, F (flow) state; ∇, T (thermodynamic) state; ■, CSTR pH and feed conditions where chemomechanical oscillations were observed in the responsive gels. The dashed zones (red in color) materialize the pH gap between the stability limits of the two states.

certain limit by the temperature or by the gel composition, but one can observe that these transitions are always the sharpest around the pKa of the acid functions.38 For example, for the MAA gels the transition is the steepest between pH 4.80 and 5.30,14 which is well in accordance with pKa = 4.88 of the monomeric analogue, 2-methylpropanoic acid. Figure 2a,b confirms that AA gels have their steepest transition 0.60 pH unit lower, between pH 4.20 and 4.70. We used another acid monomer, itaconic acid (IA)39 (Chart 1b), to be even better placed within the pH 3.0−4.5 gap. It is a dicarbonic acid, but based on the pK1 = 4.11 and pK2 = 6.29 values of its monomeric analogue, 2,2-dimethylsuccinic acid, we assume that the second carboxylate group remains protonated under the experimental conditions with the Landolt reaction and does not play a role. The swelling transitions in Figure 2c,d are related to the first deprotonation step and are the steepest between pH ∼3.60 and 4.60. Figure 2b shows that a sharp swelling−shrinking transition is obtained between pH 3.80 and 4.70 with the TB10-AA10 gels (for composition, see Table 1) at 30.0 °C, the temperature where preceding spatial dynamics studies were conducted.21,22 This swelling−shrinking characteristics fits the above-estimated pH gap between the spatial bistability limits. However, chemomechanical oscillations were never obtained under these conditions. Irrespective of [H2SO4]0, after a first contraction, the reswelling always stopped with a narrow zone that remained shrunken along the axis of the gel cylinder although the pH was around 6.0 in the CSTR. Why is there this initial failure? An answer is found in preceding studies on nonresponsive gels. Carboxylate functional groups added to the gel make the spatial bistability narrower so that it is easier easier than in the case of a neutral gelto go from one chemical state to the other by changing the gel thickness.22 At 8894



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Figure 2. pH and temperature dependence of the equilibrium radius of gel cylinders made of poly(NIPA/NTBA/AA) and poly(NIPA/NTBA/IA). The cross-linker to monomer (mol/mol) ratios are 1:222 (a, b) and 1:212 (c, d). Framed temperature values indicate where the pH characteristics are appropriate for use with the Landolt reaction. Vertical dashed lines mark the assumed pH limit of the M state in the gel.

CSTR characteristics insinuate that the pH profile near the stability limit of the F state can decline below pH 4.00 in the core of a polyelectrolyte gel. In this case, the diameter of the gel can already significantly decrease while still in the F state. This can stabilize the F state and hinder a switch to the M state. Model calculations in the stiffer BS reaction did not show such a strong declination of the F-state profile in the spatial bistability region.12 Figure 3 shows the experimental proof. It depicts the temporal variations in the diameter and length of a gel cylinder

the same time, careful observation of the CSTR behavior (Figures 2 and 9 in ref 22) reveals that the bistability shrank not only to a smaller range of control parameters (e.g., Δ[H2SO4]0 = 5 mM instead of the initial 7 mM) upon adding [PAA]0 = 0.10 M but that the stability limit of the F-state branch extended downward from pH 5.5 to 4.5 while the critical stability limit of the T-state branch was left practically unaffected. This shift can be attributed to the buffering effect of weak acids. A decrease in the amplitude of pH oscillations and shrinking the control parameter extent of the pH-bistability domain were reported for different carboxylic acids (EDTA,40 PAA,41 and acetic acid42) in other pH-clock and pH-oscillatory reactions operated in a CSTR. In other words, for the design of a chemomechanical actuator, one has to take into account that the carboxylate functional groups, necessarily present in a pHresponsive gel, unavoidably act in a similar way with respect to the spatial bistability. The two chemical states determine not only the degree of protonation of the responsive gel but also the protonation−deprotonation feedback for the chemical states of the reactive solution in the gel. On one hand, the shrinking of the spatial bistability domain, as a function of control parameters, is very advantageous because a narrower size change facilitates the cyclic switching from one chemical state to the other. On the other hand, a narrow pH gap between the F and M states requires a more accurate match of the pH response of the chemoresponsive gel. CSTR-dynamics studies can easily provide quantitative information on the above-mentioned tendencies. I remind the reader that the molar concentration of the carboxylate functional groups in pH-responsive gels is quite high, 10−90 mM, even when containing only a few mole % acid comonomers. For the preliminary studies, we needed to feed a carboxylic acid into the CSTR with a pKa value as close as possible to those in the gels. For this reason, we introduced into the feed solution a linear polyacrylamide copolymer containing 20 mol % AA. We assume that in this poly(AA/AAm), at this not very high linear charge density, the pKa remains in the 4.30−4.60 range. On the contrary, PAA homopolymers are known to have strongly pH-dependent apparent pKa values, e.g., the pKa increases from 4.50 to 5.50 between pH 3.50 and 5.50 at I = 0.10 M.43 Figure 1a−c shows how the pH values change at the limit of the F and T states of the CSTR with the Landolt reaction when increasing [−COOH]0 by feeding poly(AA/AAm). By [−COOH]0 = 20 mM, the stability limit of the F state decreased to below pH 4.00 while that of the T state remained at pH 3.00. This can explain why pH-responsive gels that start shrinking above pH 4.00 were not appropriate. The

Figure 3. Space−time plots of gel diameter (top) and length (bottom) showing the onset of the chemomechanical oscillations when entering (yellow arrows) the proper temperature range, i.e., where the pH dependence of swelling is appropriate (Figure 2d). For the space−time plots, narrow vertical sections at a given position along the cylinder axis were taken at regular time intervals and placed one after the other. Feed conditions: [KIO3]0 = 19.00 mM, [Na2SO3]0 = 60.00 mM, [H2SO4]0 = 7.083 mM, [poly(AA/AAm)]0 = 1.6 g/L, and [poly(VA/ VAc)]0 = 3.3 g/L. The constant pH in the CSTR was 5.70 ± 0.05. The video is available as Supporting Information SMovie1.

of chemical composition TB20-IA05 which is immersed in the Landolt reaction mixture in a CSTR. If the pH stability limits in the gel were the same as for the CSTR with no carboxylate functions (Figure 1a), then the gel cylinder should undergo chemomechanical oscillations at 24.4 °C, according to the pH 8895



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Figure 4. Chemomechanical oscillations obtained with a TB00-AA10 gel cylinder loaded with a glass bead. Time interval between snapshots: 11.25 min. Scale bar: 10.0 mm. Feed conditions: [KIO3]0 = 19.25 mM, [Na2SO3]0 = 60.00 mM, [H2SO4]0 = 6.875 mM, and [poly(AA/AAm)]0 = 1.6 g/L. The constant pH in the CSTR was 5.89 ± 0.03 (a, b). Oscillation periods 1 h 30 min (a) and 1 h 45 min (b). Variations in length: S min/S max = 0.617 (a) and 0.537 (b).

Figure 5. Temperature effects on the chemomechanical oscillations. Space−time plots of periodic changes in the diameter (top) and length (bottom) of the gel cylinder during the experiment in Figure 4. The video is available as Supporting Information SMovie2.

elements present in the system. We have shown that CSTR experiments can provide useful hints. Simultaneously, the chemomechanical experiments revealed that the pH-responsive gels (especially the thin ones) needed to be fed by reactant compositions that were very close to the stability limit or even not on the stable F-state branch of the CSTR without [−COOH]0. For example, the CSTR pH was 5.70 during the experiments in Figure 3, which would be in the immediate vicinity of the F-state stability limit according to Figure 1a. To stabilize the CSTR contents at these compositions, it was necessary to feed the poly(AA/AAm) linear copolymer during all chemomechanical experiments. Its high molar mass hindered it from entering the gel and provided a [−COOH]0 in the CSTR of the same order of magnitude as that inside the gels. Figures 4 and 5 show very regular chemomechanical oscillations for over 3 days, with dozens of oscillatory cycles. This extended oscillatory lifetime is a remarkable improvement compared to that of the previous BS system.14 It confirms that indeed the bromine chemistry attack on the gel chains must have been behind the drift and the final standstill in the BS synergetic chemomechanical oscillator. The chemically milder iodate chemistry does not cause such interference. This very stable and reliable operation made it possible to explore the temperature range of operation in detail with a

and temperature dependence of swelling in Figure 2d. With the reactants diffused in the gel, the M state appeared (the gel turned turbid) and the first contraction occurred, which was followed by the recovery of the chemical composition inside the gel to the F state (the gel became transparent). The gel reswelled; however, the M state did not reappear. A linear size change between the M and F states was not sufficient at 24.4 °C to obtain autonomous periodicity. Simply by decreasing the temperature to 22.4 °C in the CSTR, the gel swelled somewhat more (yellow arrows in Figure 3), which was in turn sufficient to prolong τdiff so that (τdiff + τCSTR) > τind. The M state appeared and sustained chemomechanical oscillations starting from then on. Figure 2d indicates that the gel is fully swollen only above pH 4.50 at 25 °C. If the gel in the F state really had had pH >4.50 inside, as implied by the F states in Figure 1a,b, then there would not have been such a dramatic difference between the behaviors at 24.4 and 22.4 °C. So, to get full consistency, we do need to take into account the effect of the [−COOH]0 functions in the gel and assume pH ∼3.75 for the F state of the gel, as implied by Figure 1c. Figure 2d confirms that the maximum size change occurs at 22.5 °C just within the pH gap corresponding to Figure 1c. This clearly points out that the fitting of the pH responsiveness of the gel to the pH gap in spatial bistability requires the integrated analysis of all of the 8896



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Figure 6. Chemomechanical oscillations obtained under (a) and above (b) the stoichiometric iodate/sulfite ratio with a TB20-IA05 gel cylinder loaded with a glass bead. Iodine is visualized by a PVA-based triiodide indicator (red color). Temperature: 22.2 °C. Time interval between snapshots: 50 min. Scale bar: 10.0 mm. Feed conditions: [KIO3]0 = 19.25 mM (a) and 20.50 mM (b); [Na2SO3]0 = 60.00 mM and [H2SO4]0 = 7.083 mM (a) and 6.667 mM (b); [poly(AA/AAm)]0 = 1.6 g/L; [poly(VA/VAc)]0 = 3.3 g/L. The constant pH in the CSTR was 5.75 ± 0.05 (a, b). Oscillation periods: 5 h 30 min ± 4 min (a) and 7 h 39 min ± 10 min (b). Variations in length: S min/S max = 0.576 ± 0.004 (a) and 0.501 ± 0.003 (b). The video is available as Supporting Information SMovie3.

TB00-AA10 gel cylinder. As Figure 5 reveals, the operation range was approximately ±1.0 °C around 31.0 °C. The pH and temperature dependence of the swelling degrees shown in Figure 2a confirms this very narrow temperature tolerance. At the same time, Figure 5 demonstrates the robustness of the oscillatory mode through the prompt onset of oscillations with constant period and amplitude by returning to the appropriate temperature range. We emphasize once more that it is not the chemical kinetics that is affected by such a small temperature change but the pH response of the gel that has to exactly match the pH gap between the F and M states. At 29.5 °C, the gel remained in the stationary M state (pH 4) because it was not reswollen enough to allow time for the acidautoactivated reaction to proceed inside. We can set the temperature range lower by synthesizing gels containing increasing amounts of NTBA comonomer. Figures S1 and S2 show chemomechanical oscillations in a conically shaped TB10-AA10 gel. This experiment also confirms for the case of conical geometry that the chemomechanical oscillations can be maintained for 3 days without any noticeable drift or degradation of the gel. This gel was operational at 25.8 °C, and indeed the swelling curve at 26.0 °C in Figure 2b has its swollen−shrunken transition between pH 3.75 and 2.75. Another cross-checking possibility between TB00-AA10 and TB10-AA10 gels is the linear approximation LCST = 32.5 °C − 0.460 °C/mol % NTBA that can be established for poly(NIPA/ NTBA) neutral copolymers according to Table 1 in ref 44. If the same slope can be assumed for copolymers containing a given constant amount of acid comonomer additionally to different NTBAs and considering that the TB00-AA10 gel was oscillating at 30.5 °C (Figure 4a), the TB10-AA10 gel should oscillate 4.60 °C lower, at 25.9 °C, which is the case in Figures S1 and S2. The same 4.60 °C temperature shift holds for the itaconic acid-containing gels (Figures 6 and 7) by a 10 mol % difference in the NTBA content. Sustained chemomechanical oscillations were found at 22.2 °C with the TB20-IA05 gel and at 27.2 °C for the TB10-IA05 gel. The swelling−shrinking curves in Figure 2c,d confirm these temperature values. As for the qualitative behavior of the oscillators, Figure 4a,b reveals no marked differences within the operating temperature range. Quantitatively, the period became longer (from 1 h 30 min to 1

Figure 7. Periodic traveling acid and contraction fronts in a conically shaped TB10-IA5 gel at 27.2 °C under (a) and above (b) the stoichiometric iodate/sulfite ratio. Iodine is visualized by a PVA-based triiodide indicator (red color). Time interval between snapshots: 60 min. Feed conditions: [KIO3]0 = 19.25 mM (a) and 20.50 mM (b); [Na2SO3]0 = 60.00 mM; [H2SO4]0 = 5.417 mM (a) and 5.625 mM (b); [poly(AA/AAm)]0 = 1.6 g/L; [poly(VA/VAc)]0 = 3.3 g/L. CSTR constant pH values were 6.51 ± 0.05 (a) and 6.33 ± 0.13 (b). The video is available as Supporting Information SMovie5.

h 45 min) at the 1 °C higher temperature where the gel contraction was stronger and increased amplitude (relative shrinkage to 0.537 instead of 0.617 in length) was achieved. Interestingly, in these synergetic oscillators there is no imposed period andwhich is also very importantno imposed pH−time profiles either. The time−space plots of the diameter changes reveal (Figures 3, 5, and 9 top rows) that the shrinking phase results in much faster than the swelling phase in these synergetic systems. A similar abrupt shrinking phase and a slow reswelling phase were found with the BS reaction (Figure 13 in ref 14). As the reacting medium becomes acidic first in the middle of the gel, the network starts contracting from the inside, letting the solvent leave the gel unhindered. Even though the chemical reaction is fast, the growth of an acid front propagating from inside introduces fewer mechanical constraints on the shrinking of the gel compared to the case when a sudden concentration change in the environment is generated by an oscillatory reaction or by a manual change of the external solvent composition. It can be an advantage for several practical applications that no shrinkage barrier45 effect and no skin formation develop in synergetictype chemomechanical oscillators. It can be clearly observed in Figure 6a that the gel cylinder becomes acidic first in the middle and the M state propagates outward and along the axis. The slight dumbbell shape of the turbid region (3rd, 10th, and 8897



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by relying on shadowscopy, whereas the red triiodide−PVA complex can clearly be seen in the direct view. In both the gel cylinder and gel cone, the iodine front always follows behind the propagating acid (turbid) front. A similar spatial distribution was observed in reaction−diffusion patterns with the FIS46 and TuIS47 mixed Landolt reactions in agarose gels. During the return to the F state in the gel, the turbid zone needs more time to disappear (Figures 7 and 8) and the longitudinally contracted state lasts longer (Figures 6 and 9) if

17th slices) is caused by the simultaneous contraction that also started in the middle, where the M state appeared first. As the front propagation is much faster, finally a uniformly contracted gel cylinder is attained (4th, 11th, and 18th slices). The return to the F state occurs then “as normally” from outside, from where the fresh reactants enter the gel, as the fading away of the turbid region shows it in the next slices. Owing to this sequence, buckling of the outer part of the gel occurs during reswelling. This can be best observed in the shadowscopic views in Figures 6b and 7, latter for the conical shape. The still contracted and much less elastic inner part hinders the gel from isotropically swelling, that is, in length. So the swollen outer annular zone is compressed in the axial direction until gel elongation starts. With the IS reaction, the M and F states, respectively, are strongly in phase along the gel cylinder; therefore, the glass weight is lifted and lowered by large amplitudes. In the BS reaction, the M state was more likely to appear at one of the extremities of the cylinder where, as assumed, the uniform and intensive stirring around the gel is very slightly impaired by the glued objects.14 Other aspects of the front propagation, contraction, and reswelling are quite similar in the BS and IS reactions, especially for the conical shape (Figures 7 and 8).

Figure 9. Space−time plots of the periodic changes in the diameter (top) and length (bottom) of the gel cylinder at increasing iodate/ sulfite feed ratios. For other experimental conditions, see Figure 6. The video is available as Supporting Information SMovie3.

Figure 8. Space−time plot of the oscillations in Figure 7. Periods: 8 h 15 min ± 40 min and 7 h 23 min ± 23 min under and above the stoichiometric iodate/sulfite ratio, respectively. The video is available as Supporting Information SMovie5.

the reactant feed ratio is above the stoichiometric ratio. Not only is proportionally less HSO3− fed but iodine must also be consumed in a redox reaction in addition to the neutralization of the acid. The gel diameter (Figure 9) at [KIO3]0/[Na2SO3]0 < 0.333 is quasiconstant while the turbid zone is present and increases quasilinearly thereafter, until the next contraction. The diameter oscillations show a ramp waveform in time. At the same time, the length oscillations are symmetric and have a triangle profile, so the lifting and lowering of the weight are continuous and occur at the same rate. At [KIO3]0/[Na2SO3]0 > 0.333, the rate is still the same up and down, but the gel stays at its fully contracted length for a long time. The waveform is more squarelike. The diameter oscillations follow a somewhat complex ramp. The diameter increase drops a little at the moment when the elongation starts. It becomes clear from the overlaid shadowscopic and direct view images (top row in Figure 9) that elongation starts only after the full consumption of iodine. A rigid axis forms with iodine, and the deformation under the stress exerted by the glass bead is independent of the thickness of the iodine zone. This means that the elastic modulus of the gel falls by more than 1 order of magnitude at the moment when iodine disappears. Alternatively, the amount

Besides the temperature, the effect of the iodate/sulfite ratio around the stoichiometric composition (0.333) was studied in both the cylindrical and conical geometries. Comparing parts a and b in Figures 6 and 7, some qualitative differences can be discovered depending on having the sulfite or the iodate in excess, respectively. The red color in Figures 6b and 7b shows the spatial distribution of triiodide ions (I2 + I−) in the M state that form when iodine is an end product as indicated in eq R2. On the contrary, when iodine is only an intermediate in the IS reaction, its concentration remains below the limit of detection. The slightly orange color in the shadowscopic view in Figure 6a is not due to the triiodide−PVA complex but is due to light scattering. White light is shined through the gel in the direction of the camera in the shadowscopic imaging, so zones in the early stage of phase separation appear orange in this view because of the missing scattered blue component. At advanced contraction, the wavelength dependence of the light scattering diminishes, and the gel is not transparent any more so it appears dark inside. The same could explain the yellowish color of the propagating acid front in the conical gel geometry in Figure 7. In this geometry, Figure 7a,b cannot be distinguished 8898



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Notes

of iodine could be constant by assuming that the red zone is only a ring behind the acid front. Under the stoichiometric [KIO3]0/[Na2SO3]0 ratio, the elastic modulus of the gel was decreasing proportionally with decreasing thickness of the turbid zone. Figure 5 shows for the case [KIO3]0/[Na2SO3]0 < 0.333 in which the triangle profile of the length changes passes to a sawtooth profile when the system is closer to the hightemperature limit of operation (stronger contraction that starts at a little higher pH). Consequently, by finely tuning the experimental conditions, triangle, square, or sawtooth waveform length oscillations can be produced by choice with the IS synergetic chemomechanical oscillator.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I thank Patrick De Kepper for critically reading the manuscript. Financial support is acknowledged from the CNRS and from the Mobility program (MB08A-80244) of the Hungarian Research and Technology Innovation Fund (KTIA), the National Development Agency (NFÜ ), the Hungarian Research Fund (OTKA), and the EU FP7 Marie Curie Cofund Action.

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CONCLUSIONS Synergetic chemomechanical oscillators are a new class of chemomechanical actuators. Among the three acid-driven examples provided until now, only that presently reported is capable of exhibiting large-amplitude (almost a factor of 2 in linear size) oscillations over several days without significant drift. The key steps in obtaining synergetic chemomechanical oscillations with this Landolt reaction are the following: (1) identifying that the pH at the stability limit of the F state shifts to lower values (from pH ∼5.5 to below 4.0) in the presence of carboxylic acids, such as the functional groups in the pHresponsive gel, due to the pH-buffering effect of the weak acid functions; (2) stabilizing the CSTR F state near this lowered pH limit by adding a high-molar-mass polyacrylate copolymer to the feed that does not enter the gel and maintains a carboxylate concentration in the CSTR of the same order of magnitude as inside the pH-responsive gel; (3) the fine tuning of the gel’s pH response into the range of pH 2.75−3.75 by using appropriate combinations of acid and hydrophobic comonomers and by finely adjusting the temperature. To further generalize the development of this new class of chemomechanical oscillators, their observations in quite different systems would be instructive and useful for any envisioned application.48,49 This includes exploiting alkalineproducing reactions50 or metal ion concentration changes generated via complexons.40 We believe that developing metalion-driven systems will resolve the problem of the very narrow operational temperature range that also turned out to be a major inconvenience of using pH-responsive gels. Studying the operating conditions and behavior of synergetic chemomechanical oscillators of a larger chemical variety should bring about a clearer view of the universal properties that have to be met in the system to produce sustained autonomous actuation operations. The accumulated experience could open the way for constructing such synergetic oscillators with more delicate reactions, e.g., in an enzymatic system51 operated in bioelastic materials.

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ASSOCIATED CONTENT

S Supporting Information *

Chemomechanical oscillations in conically shaped gels. Movies showing the chemomechanical oscillations of Figures 3−9 at 7000× speed. This material is available free of charge via the Internet at http://pubs.acs.org.

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Sustained Large-Amplitude Chemomechanical Oscillations Induced

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