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Chemical Pumps and Flexible Sheets Spontaneously Form Self-Regulating Oscillators in Solution

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Chemical Pumps and Flexible Sheets Spontaneously Form Self-Regulating Oscillators in Solution Chemical pumps and flexible sheets spontaneously form self-regulating oscillators in solution Raj Kumar Mannaa, Oleg E. Shklyaeva, and Anna C. Balazsa,1 aDepartment of Chemical Engineering, University of Pittsburgh, Pittsburgh, PA 15260 Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved February 13, 2021 (received for review November 4, 2020) The synchronization of self-oscillating systems is vital to various active sheets encompass a level of autonomous spatiotemporal biological functions, from the coordinated contraction of heart activity that extends the limited repertoire of self-oscillating soft muscle to the self-organization of slime molds. Through modeling, materials and facilitates the fabrication of autonomous, self- we design bioinspired materials systems that spontaneously form regulating soft robots. shape-changing self-oscillators, which communicate to synchro- The mechanism driving the oscillatory, shape-changing be- nize both their temporal and spatial behavior. Here, catalytic re- havior involves a distinctive combination of chemomechanical actions at the bottom of a fluid-filled chamber and on mobile, transduction, the confinement of the host fluid, and a feedback flexible sheets generate the energy to “pump” the surrounding loop. Fig. 1A shows the key components in the system: a fluid- fluid, which also transports the immersed sheets. The sheets exert filled chamber that contains a surface-anchored catalytic patch a force on the fluid that modifies the flow, which in turn affects and a deformable sheet (Fig. 1A). A fixed concentration of re- the shape and movement of the flexible sheets. This feedback actants is added to the solution to initiate the catalytic reaction enables a single coated (active) and even an uncoated (passive) at the central patch. The energy released from this reaction is sheet to undergo self-oscillation, displaying different oscillatory converted into the mechanical motion (flow) of the surrounding modes with increases in the catalytic reaction rate. Two sheets fluid. This constitutes the chemomechanical transduction vital to (active or passive) introduce excluded volume, steric interactions. the observed behavior. Since the system is symmetric about the This distinctive combination of the hydrodynamic, fluid–structure, central patch, the fluid flow occurs about each side of this patch and steric interactions causes the sheets to form coupled oscilla- (Fig. 1A). These symmetric streams eventually hit the confining tors, whose motion is synchronized in time and space. We develop walls, driving the fluid to circulate and form two convective rolls APPLIED PHYSICAL SCIENCES a heuristic model that rationalizes this behavior. These coupled (as detailed in the results section). Hence, the confinement of self-oscillators exhibit rich and tunable phase dynamics, which de- the fluid is another critical component for these self-oscillations. pends on the sheets’ initial placement, coverage by catalyst and The third critical component is the feedback loop that arises relative size. Moreover, through variations in the reactant concen- from the fluid–structure interactions between the circulating tration, the system can switch between the different oscillatory fluid and the compliant sheet (whether the sheet is passive or modes. This breadth of dynamic behavior expands the functional- chemically active). The fluid transports the sheet within the ity of the coupled oscillators, enabling soft robots to display a chamber, but this sheet also exerts a force on the fluid that variety of self-sustained, self-regulating moves. modifies the flow. The modified flow in turn affects the move- ment of the sheet. This feedback mechanism contributes to the chemically active | reconfigurable sheets | self-oscillating system | oscillatory behavior; the magnitude of the effect depends on the shape-changing coupled oscillators | spatiotemporal synchronization geometry and flexibility of the sheet. The examples below illustrate of coupled oscillators Significance elf-oscillating chemical reactions transduce a constant, non- Speriodic input of energy into sustained periodic motion. Such Using computational modeling, we designed a self-oscillating self-oscillating chemistry is resplendent in biology, enabling the materials system that is driven by a nonperiodic chemical re- firing of neurons, the beating of the heart, and the cyclic be- action to undergo both periodic shape changes and motion. havior of predator–prey relationships (1). The development of Catalytic reactions in a fluid-filled microchamber drive the self-oscillating, shape-changing materials would hasten the de- movement of the fluid and immersed flexible sheets. The fluid velopment of soft robots that autonomously perform self-sustained affects the sheets’ shape, and the sheets affect the fluid flow. work and controllable movement (2, 3). With few exceptions (4–6), This feedback enables remarkably rich and controllable oscil- however, the creation of synthetic self-oscillating materials re- latory behavior: a single sheet fishtails periodically across the mains a significant challenge. Most candidate soft materials only chamber or circulates continuously within a narrow region. exhibited periodic behavior when exposed to variations in the Two sheets form coupled oscillators displaying not only syn- constant energy input (e.g., from changes in illumination, heat, chronized temporal behavior, but also unique, coordinated humidity, or pH) (7–12). The rare exceptions include soft ma- morphological reconfigurations. These oscillators enable de- terials that incorporate one of three intrinsically self-oscillatory velopment of soft robots that operate through an inherent chemical reactions, e.g., self-oscillating gels driven by the Belouzov– coupling of chemistry and motion, permitting novel autono- Zhabotinsky reaction (13–17). Herein, we use computational mod- mous and self-regulating behavior. eling to design chemically driven, flexible micro- to millimeter-sized sheets powered by nonoscillatory chemical reactions that form Author contributions: R.K.M., O.E.S., and A.C.B. designed research, performed research, self-oscillating, shape-changing systems in solution. A single two- analyzed data, and wrote the paper. dimensional sheet spontaneously morphs into a three-dimensional The authors declare no competing interest. structure that moves periodically in time. Two sheets form cou- This article is a PNAS Direct Submission. pled oscillators that communicate to synchronize both their mo- Published under the PNAS license. tion and morphology. While biological and synthetic systems can 1To whom correspondence may be addressed. Email: [email protected]. exhibit self-organized motion and synchronization, there are few This article contains supporting information online at https://www.pnas.org/lookup/suppl/ systems that exhibit coordinated spatial movement, structural doi:10.1073/pnas.2022987118/-/DCSupplemental. change, and temporal synchronization (18). These responsive, Published March 15, 2021. PNAS 2021 Vol. 118 No. 12 e2022987118 https://doi.org/10.1073/pnas.2022987118 | 1of8 Downloaded by guest on September 27, 2021 Fig. 1. Self-oscillations of a passive sheet. (A) Schematic of the fluidic chamber containing a chemical pump (marked by red rectangular region) and a passive elastic sheet (in blue). (Inset) The network of nodes (marked by blue dots) that form the sheet and the flexible bonds between nodes (white lines). Stretching 2 and bending moduli of the sheet are κs = 60pN and κb = 7.2pNmm , respectively. The sheet is 1.95mm30.6mm30.26mm in size. (B) Low reaction rate: patch −2 −1 rm = 52μmol m · s (Movie S1). Black arrows indicate the direction and magnitude of the fluid flow; the arrows on the left vertical wall reveal the flows within a vertical plane passing through the center of the chamber. Arrows on the right sidewall indicate the flow in the orthogonal vertical plane. Color bar indicates the concentration of H2O2 in the solution. (C) Height (zs) of the center of the sheet. Color bar indicates time. (D and E) High reaction rate: patch −2 −1 rm = 72μmol m · s .(F) Center of the sheet oscillates back and forth across the catalytic pump. (G and H) At the highest reaction rate, patch −2 −1 rm = 96μmol m · s , the sheet simply circulates within the right half of the domain. (I) Corresponding temporal motion of the center of the sheet. Times for the sheet configurations are marked on the bottom of the rightmost column. the complex dynamics that emerges due to interactions of these for the observed pumping velocities in a number of systems in- three critical components and provide new systems for uncov- volving catalytic patches on an immobile surface and mobile, ering factors that regulate nonequilibrium behavior. spherical particles (chemical motors) (20–22). For example, we predicted and confirmed experimentally that catalytic reactions Computational Model on the bottom wall of a chamber generate solutal buoyance forces, The surface-anchored catalytic patch (Fig. 1A) works as a which deliver microparticle cargo to specified regions in micro- “ ” chemical pump that drives the fluid flows along the bottom chambers and consequently, the cargo is deposited around a surface toward or away from the patch, depending on the nature specific position on the surface (22). We also predicted and ex- of the chemical reaction. This flow occurs due to solutal buoyancy perimentally validated that the coordination among three enzy- (19, 20).
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