Pattern Formation and Shape Changes in Self-Oscillating Polymer Gels

Synthetic homeostatic materials with chemo-mechano-chemical self-regulation

Living organisms have unique homeostatic abilities, maintaining tight control of their local environment through interconversions of chemical and mechanical energy and self-regulating feedback loops organized hierarchically across many length scales. In contrast, most synthetic materials are incapable of continuous self-monitoring and self-regulating behaviour owing to their limited single-directional chemomechanical or mechanochemical modes. Applying the concept of homeostasis to the design of autonomous materials would have substantial impacts in areas ranging from medical implants that help stabilize bodily functions to 'smart' materials that regulate energy usage. Here we present a versatile strategy for creating self-regulating, self-powered, homeostatic materials capable of precisely tailored chemo-mechano-chemical feedback loops on the nano- or microscale. We design a bilayer system with hydrogel-supported, catalyst-bearing microstructures, which are separated from a reactant-containing 'nutrient' layer. Reconfiguration of the gel in response to a stimulus induces the reversible actuation of the microstructures into and out of the nutrient layer, and serves as a highly precise 'on/off' switch for chemical reactions. We apply this design to trigger organic, inorganic and biochemical reactions that undergo reversible, repeatable cycles synchronized with the motion of the microstructures and the driving external chemical stimulus. By exploiting a continuous feedback loop between various exothermic catalytic reactions in the nutrient layer and the mechanical action of the temperature-responsive gel, we then create exemplary autonomous, self-sustained homeostatic systems that maintain a user-defined parameter--temperature--in a narrow range. The experimental results are validated using computational modelling that qualitatively captures the essential features of the self-regulating behaviour and provides additional criteria for the optimization of the homeostatic function, subsequently confirmed experimentally. This design is highly customizable owing to the broad choice of chemistries, tunable mechanics and its physical simplicity, and may lead to a variety of applications in autonomous systems with chemo-mechano-chemical transduction at their core.

Mechano-chemical oscillations and waves in reactive gels

We review advances in a new area of interdisciplinary research that concerns phenomena arising from inherent coupling between non-linear chemical dynamics and mechanics. This coupling provides a route for chemical-to-mechanical energy transduction, which enables materials to exhibit self-sustained oscillations and/or waves in both concentration and deformation fields. We focus on synthetic polymer gels, where the chemo-mechanical behavior can be engineered into the material. We provide a brief review of experimental observations on several types of chemo-mechanical oscillations in gels. Then, we discuss methods used to theoretically and computationally model self-oscillating polymer gels. The rest of the paper is devoted to describing results of theoretical and computational modeling of gels that undergo the oscillatory Belousov-Zhabotinsky (BZ) reaction. We discuss a remarkable form of mechano-chemical transduction in these materials, where the application of an applied force or mechanical contact can drive the system to switch between different dynamical behavior, or alter the mechanical properties of the material. Finally, we discuss ways in which photosensitive BZ gels could be used to fabricate biomimetic self-propelled objects. In particular, we describe how non-uniform illumination can be used to direct the movement of BZ gel 'worms' along complex paths, guiding them to bend, reorient and turn.

Post-self-assembly cross-linking of molecular nanofibers for oscillatory hydrogels

After a polymerizable hydrogelator self-assembles in water to form molecular nanofibers, post-self-assembly cross-linking allows the catalyst of the Belousov-Zhabotinsky (BZ) reaction to be attached to the nanofibers, resulting in a hydrogel that exhibits concentration oscillations, spiral waves, and concentric waves. In addition to the first report of the observation of BZ spiral waves in a hydrogel that covalently integrates the catalyst, we suggest a new approach to developing active soft materials as chemical oscillators and for exploring the correlation between molecular structure and far-from-equilibrium dynamics.

Excitatory and inhibitory coupling in a one-dimensional array of Belousov-Zhabotinsky micro-oscillators: theory

We study numerically the behavior of one-dimensional arrays of aqueous droplets containing the oscillatory Belousov-Zhabotinsky reaction. Droplets are separated by an oil phase that allows coupling between neighboring droplets via two species: an inhibitor, Br(2), and an activator, HBrO(2). Excitatory coupling alone (through the activator) generates in-phase oscillations and/or "waves," while inhibitory coupling alone (through Br(2)) gives rise to antiphase oscillations, Turing patterns, and their combinations. The simultaneous presence of excitatory and inhibitory coupling leads to a large number of new spatiotemporal patterns, including some that exhibit very complex behavior. Analysis of a simple model allows us to simulate patterns resembling those observed experimentally under similar conditions and to elucidate the contributions of droplet and gap sizes, activator and inhibitor partition coefficients, and malonic acid concentration to the coupling strengths.

Using mesoscopic models to design strong and tough biomimetic polymer networks

Using computational modeling, we investigate the mechanical properties of polymeric materials composed of coiled chains, or "globules", which encompass a folded secondary structure and are cross-linked by labile bonds to form a macroscopic network. In the presence of an applied force, the globules can unfold into linear chains and thereby dissipate energy as the network is deformed; the latter attribute can contribute to the toughness of the material. Our goal is to determine how to tailor the labile intra- and intermolecular bonds within the network to produce material exhibiting both toughness and strength. Herein, we use the lattice spring model (LSM) to simulate the globules and the cross-linked network. We also utilize our modified Hierarchical Bell model (MHBM) to simulate the rupture and reforming of N parallel bonds. By applying a tensile deformation, we demonstrate that the mechanical properties of the system are sensitive to the values of N(in) and N(out), the respective values of N for the intra- and intermolecular bonds. We find that the strength of the material is mainly controlled by the value of N(out), with the higher value of N(out) providing a stronger material. We also find that, if N(in) is smaller than N(out), the globules can unfold under the tensile load before the sample fractures and, in this manner, can increase the ductility of the sample. Our results provide effective strategies for exploiting relatively weak, labile interactions (e.g., hydrogen bonding or the thiol/disulfide exchange reaction) in both the intra- and intermolecular bonds to tailor the macroscopic performance of the materials.

Role of parallel reformable bonds in the self-healing of cross-linked nanogel particles

We develop a hybrid computational approach to examine the mechanical properties and self-healing behavior of nanogel particles that are cross-linked by both stable and labile bonds. The individual nanogels are modeled via the lattice spring model (LSM), which is an effective method for probing the response of materials to mechanical deformation. The cross-links between the nanogels are simulated via the hierarchical Bell model (HBM), which allows us to capture the rupturing of multiple parallel bonds as the result of an applied force. Because the labile bonds are relatively reactive, they can reform after they have been ruptured. To incorporate the possibility of bonds reforming, we modify the HBM formalism and validate the modified HBM by considering a system of two surfaces, which are connected by multiple parallel bonds. We then use our hybrid HBM/LSM to simulate the behavior of the cross-linked nanogels under a tensile deformation. In these simulations, each labile linkage between the nanogels contains at most N parallel bonds. We vary the fraction of labile linkages and the value of N in these linkages to determine the optimal conditions for improving the robustness of the material. Although numerous parallel bonds within a linkage enhance the strength of the material, these bonds diminish the ductility and the ability of the material to undergo the structural rearrangements that are necessary for self-repair. For a relatively low fraction of labile bonds and N ≤ 4, however, we can significantly improve the strength of the material and preserve the self-healing properties. For instance, a sample with 30% labile linkages and N = 4 per linkage is roughly 200% stronger than a sample that is cross-linked solely by stable bonds and can still undergo self-repair in response to the tensile deformation. The results reveal how mechanical stress can lead not only to the appearance of cavities within the material but also to bond formation that "heals" these cavities and thus prevents the catastrophic failure of the material.

Photoinduced proton transfer in a pyridine based polymer gel

We describe an experimental and theoretical consideration of photoexcited proton transfer in a poly(4-vinyl pyridine)/pyridine gel. Evidence was found for two states of a multiple state process analyzed by DFT modeling. According to the latter, following irradiation at 385 nm, the proton donor is the CH group of the polymer main chain and the proton acceptor is the nitrogen of the polymeric pyridine side chain. Proton transfer is made possible through the assistance of a mobile pyridine solvent molecule acting as a transfer vehicle. Proton transfer promotes both a geometrical rearrangement of the vinyl side chain as well as electronic density redistribution. The photoproduct intermediate-the hydrogen-bonded complex between the protonated solvent pyridine molecule and the deprotonated polymeric pyridine side chain-is identified by its Curie law magnetic susceptibility, ESR spectrum, and fluorescence lifetime measurements. The proton transfer from the nitrogen of the solvent pyridine molecule to the pyridine side chain nitrogen, producing pyridinium, is a thermodynamically favorable relaxation process and occurs without an energy barrier. The protonation of nitrogen on the polymeric side chain was detected by solid state NMR spectroscopy performed on a (15)N-polymer enriched gel. The calculations and experimental data suggest a central role for the gel solvent molecule as a catalytic agent and proton transfer vehicle. The process suggested by DFT modeling may have relevance for photosensitive devices in part due to the fact that we have been able to show that long-lived paramagnetism may be included among the inducible properties of soft polymer gels.

Emergent, collective oscillations of self-mobile particles and patterned surfaces under redox conditions

We have discovered that silver chloride (AgCl) particles in the presence of UV light and dilute hydrogen peroxide exhibit both single-particle and collective oscillations in their motion which arise due to an oscillatory, reversible conversion of AgCl to silver metal at the particle surface. This system exhibits several of the hallmarks of nonlinear oscillatory reactions, including bistability, reaction waves, and synchronized collective oscillations at high particle concentrations. However, unlike traditional oscillatory reactions that take place among dispersed solute species in solution or near a fixed electrode surface, this system of self-mobile catalytic particles evinces a new dynamical length scale: the interparticle spacing, which appears to control wave propagation. The collective motions of these powered nanoparticles self-organize into clumped oscillators with significant spatiotemporal correlations between clumps. A variant of this system using a regular array of lithographically patterned silver disks supports the propagation of binary "On/Off" Ag/AgCl waves through the lattice.

Self-oscillating gels driven by the Belousov-Zhabotinsky reaction as novel smart materials

So far stimuli-responsive polymer gels and their application to smart materials have been widely studied; this research has contributed to progress in gel science and engineering. For their development as a novel biomimetic polymer, studies of polymers with an autonomous self-oscillating function have been carried out since the first reports in 1996. The development of novel self-oscillating polymers and gels have been successful utilizing the oscillating reaction, called the Belousov-Zhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. The self-oscillating polymer is composed of a poly(N-isopropylacrylamide) network in which the catalyst for the BZ reaction is covalently immobilized. In the presence of the reactants, the polymer undergoes spontaneous cyclic soluble-insoluble changes or swelling-deswelling changes (in the case of gel) without any on-off switching of external stimuli. Potential applications of the self-socillating polymers and gels include several kinds of functional material systems, such as biomimetic actuators and mass transport surface.

Active polymer gel actuators

Many kinds of stimuli-responsive polymer and gels have been developed and applied to biomimetic actuators or artificial muscles. Electroactive polymers that change shape when stimulated electrically seem to be particularly promising. In all cases, however, the mechanical motion is driven by external stimuli, for example, reversing the direction of electric field. On the other hand, many living organisms can generate an autonomous motion without external driving stimuli like self-beating of heart muscles. Here we show a novel biomimetic gel actuator that can walk spontaneously with a worm-like motion without switching of external stimuli. The self-oscillating motion is produced by dissipating chemical energy of oscillating reaction. Although the gel is completely composed of synthetic polymer, it shows autonomous motion as if it were alive.

Spatial confinement controls self-oscillations in polymer gels undergoing the Belousov-Zhabotinsky reaction

Chemoresponsive gels undergoing the Belousov-Zhabotinsky (BZ) reaction exhibit self-sustained pulsations, which can be harnessed to perform mechanical work. In technological applications, the gels would typically be confined between hard surfaces and thus, it is essential to establish how confinement affects these distinctive oscillations. Using theory and simulation, we pinpoint regions in phase space where the dynamic behavior of BZ gels critically depends on the presence of confining walls. We then illustrate how the wave propagation within thin samples can be tailored by selectively introducing "cut outs" in the bounding surfaces. The oscillations in the latter films are localized in specified areas, so the system contains well-defined oscillatory and nonoscillatory regions. The cut outs provide an effective means of tuning the mechanical action within the film and provide a route for tailoring the functionality of the material.

Harnessing labile bonds between nanogel particles to create self-healing materials

Using computational modeling, we demonstrate the self-healing behavior of novel materials composed of nanoscopic gel particles that are interconnected into a macroscopic network by both stable and labile bonds. Under mechanical stress, the labile bonds between the nanogels can break and readily re-form with reactive groups on neighboring units. This breaking and re-forming allows the units in the network to undergo a structural rearrangement that preserves the mechanical integrity of the sample. The simulations show that just a small fraction of labile bonds leads to a roughly 25% increase in the stress needed to induce fracture. Thus, the labile bonds can significantly improve the tensile strength of the material. The findings provide guidelines for creating high-strength, self-healing materials.

Using light to guide the self-sustained motion of active gels

We undertake the first computational study to determine the effect of light on polymer gels undergoing the Belousov-Zhabotinsky (BZ) reaction. The BZ gels are unique materials because they can undergo rhythmic mechanical oscillations in the absence of external stimuli. The BZ reaction, however, is photosensitive. Via simulations, we demonstrate that the interplay between the chemoresponsive gels and the photosensitive reaction can cause millimeter sized BZ gels to exhibit autonomous, directed motion or reorientation away from 4 the light. In effect, we show that these synthetic BZ "worms" display a fundamental biomimetic behavior: movement away from an adverse environmental condition, which in the context of the BZ reaction is the presence of light.

Controlling chemical oscillations in heterogeneous Belousov-Zhabotinsky gels via mechanical strain

We performed theoretical and computational studies to determine the effect of an applied mechanical strain on the dynamic behavior of heterogeneous polymer gels undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. In these spatially heterogeneous gels, the catalyst for the reaction is localized in specific patches within the polymer network and the BZ reaction only occurs within these catalyst-containing patches, which we refer to as BZ patches. We focused on a model for a one-dimensional system, and further assumed that the BZ reaction did not affect the degree of swelling within the gel. For gels having one and two BZ patches, we found that a tensile or compressive strain could induce transitions between the oscillatory and nonoscillatory, steady-state regimes of the system. For certain values of the BZ stoichiometric parameter f , these transitions could exhibit a hysteresis. In systems having two oscillating BZ patches, an applied strain could cause a switching between the in-phase and out-of-phase synchronization of the oscillations. The ability to controllably alter the dynamic behavior of BZ gels through mechanical deformations opens up the possibility of using these materials in the design of chemo-mechanical sensors.

Nonequilibrium microstructures in reactive monolayers as soft matter systems

Chemical systems provide classical examples of nonequilibrium pattern formation. Reactions in weak aqueous solutions, such as the extensively investigated Belousov-Zhabotinsky reaction, demonstrate a rich variety of patterns, ranging from travelling fronts to rotating spiral waves and chemical turbulence. Pattern formation in such systems is based on interplay between the reactions and diffusion. Intrinsically, this puts a restriction on the minimum length scale of the developing structures, which cannot be shorter than the diffusion length of the reactants. However, much smaller nonequilibrium structures, with characteristic lengths reaching down to nanoscales, are also possible. They are found in reactive soft matter, where energetic interactions between molecules are present as well. In these systems, chemical reactions and diffusion interfere with phase transitions, yielding active, stationary or dynamic microstructures. Nonequilibrium soft-matter microstructures are of fundamental importance for biological cells and may have interesting engineering applications. In this Minireview, we focus on the microstructures found in reactive soft-matter monolayers at solid surfaces or liquid-air interfaces.

Influences of periodic mechanical deformation on spiral breakup in excitable media

Influences of periodic mechanical deformation (PMD) on spiral breakup that results from Doppler instability in excitable media are investigated. We present a new effect: a high degree of homogeneous PMD is favored to prevent the low-excitability-induced breakup of spiral waves. The frequency and amplitude of PMD are also significant for achieving this purpose. The underlying mechanism of successful control is also discussed, which is believed to be related to the increase of the minimum temporal period of the meandering spiral when the suitable PMD is applied.

Three-dimensional model for chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction

We develop a computational model to capture the complex, three-dimensional behavior of chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. The model combines components of the finite difference and finite element techniques and is an extension of the two-dimensional gel lattice spring model recently developed by two of us [V. V. Yashin and A. C. Balazs, J. Chem. Phys. 126, 124707 (2007)]. Using this model, we undertake the first three-dimensional (3D) computational studies of the dynamical behavior of chemoresponsive BZ gels. For sufficiently large sample sizes and a finite range of reaction parameters, we observe regular and nonregular oscillations in both the size and shape of the sample that are coupled to the chemical oscillations. Additionally, we determine the critical values of these reaction parameters at the transition points between the different types of observed behavior. We also show that the dynamics of the chemoresponsive gels drastically depends on the boundary conditions at the surface of the sample. This 3D computational model could provide an effective tool for designing gel-based, responsive systems.

The transition from pH waves to iodine waves in the iodate/sulfite/thiosulfate reaction-diffusion system

Nonlinear spatial temporal behavior of the iodate/thiosulfate/sulfite reaction is investigated both in a stirred and spatially extended media. In accord with the temporal dynamics in the homogeneous media, both propagating fronts and target patterns are achieved in the spatially extended medium. On increasing the iodate concentration the system evolves from exhibiting propagating fronts to circular waves and then shows target patterns and finally the iodine waves. Influences of concentrations of sulfite, thiosulfate and acid on the reaction kinetics and pattern formation are also investigated systematically, and transitions from pH waves to iodine waves can be achieved via adjusting the concentration of the three species. The propagation velocities of pH and iodine waves are understood with the quadratic and cubic autocatalysis of proton and iodide respectively.

Chemomechanical synchronization in heterogeneous self-oscillating gels

Using computational modeling, we introduce patches of self-oscillating gels undergoing the Belousov-Zhabotinsky (BZ) reaction into a nonreactive polymer network and thereby demonstrate how these BZ gels can be harnessed to impart remarkable functionality to the entire system. By first focusing on two adjacent patches of BZ gels, we show that the patches' oscillations can become synchronized in phase or out of phase, with the oscillation frequency depending on the synchronization mode and the spatial separation between these domains. We then apply these results to an array of five adjacent BZ patches and by varying the distance between these pieces, we dramatically alter the dynamical behavior of the patterned gel. For example, the sample can be made to exhibit a unidirectional traveling wave or display a concerted expansion and contraction, properties that are valuable for creating gel-based devices, such as micropumps and microactuators. The findings point to a "modular" design approach, which can impart different functionality simply by arranging identical pieces of BZ gels into distinct spatial arrangements within a polymer matrix.

Mechanically induced chemical oscillations and motion in responsive gels

Mechanochemical transduction plays a vital role in biological processes. There have, however, been few studies on exploiting mechanical stimuli to trigger chemical signals in non-biological systems. Using computational modeling, we investigate how an applied mechanical pressure can be harnessed to initiate traveling chemical waves in polymer gels undergoing the Belousov-Zhabotinsky (BZ) reaction. We uncover a rich dynamic behavior, isolating systems where the applied pressure induces chemical oscillations in an initially non-oscillatory system. We also pinpoint a scenario where the compression induces both oscillations and the autonomous rotation of the entire sample. Determining factors that control mechanochemical transduction in BZ gels is necessary for establishing guidelines to create self-adjusting or adaptive materials that not only "sense" a localized impact, but also transmit a global chemical signal in response to the local mechanical perturbation. Such materials can potentially be used to fabricate touch-sensitive sensors and membranes, as well as self-reinforcing materials.

Theoretical and computational modeling of self-oscillating polymer gels

The authors model wave propagation in swollen, chemoresponsive polymer gels that are undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. To carry out this study, they first modify the Oregonator model for BZ reactions in simple solutions to include the effect of the polymer on the reaction kinetics. They then describe the gel dynamics through the framework of the two-fluid model. The polymer-solvent interactions that are introduced through the BZ reaction are captured through a coupling term, which is added to the Flory-Huggins model for polymer-solvent mixtures. The resulting theoretical model is then used to develop the gel lattice spring model (gLSM), which is a computationally efficient approach for simulating large-scale, two-dimensional (2D) deformations and chemical reactions within a swollen polymer network. The 2D calculations allow the authors to probe not only volume changes but also changes in the sample's shape. Using the gLSM, they determine the pattern formation and shape changes in 2D rectangular BZ gels that are anchored to a solid wall. They demonstrate that the dynamic patterns depend on whether the gel is expanded or contracted near the wall, and on the sample's dimensions. Finally, they isolate a scenario where the detachment of the gel from the wall leads to macroscopic motion of the entire sample.