Chemomechanical Oscillations Research Articles

Novel Approach to Increasing the Amplitude of the Mechanical Oscillations of Self-Oscillating Gels: Introduction of Catalysts Both as Pendant Groups and as Crosslinkers

For the first time, we introduced chemomechanical self-oscillating poly(N-isopropylacrylamide)-based gels containing catalytically active Fe or Ru complexes both as crosslinkers and as pendant groups. All the obtained gels exhibited sustained autonomous oscillations driven by the Belousov–Zhabotinsky reaction within their structure. The Ru complex-based gels also demonstrated pronounced chemomechanical oscillations; they periodically swelled/shrunk when the catalyst was reduced/oxidized. It was found that the combination of catalytically active cross-linking and pendant Ru complexes in the same gel led to a change in the structure of the gel and a significant increase in the amplitude of its mechanical oscillations. The proposed approach allowed for increasing the amplitude of the mechanical oscillations of self-oscillating gels and opened up new possibilities for adjusting their characteristics. We believe that these gels hold potential for the development of soft actuators and systems capable of signal processing through propagating and interacting chemical waves.

On phase correspondence between chemical oscillations in liquid Belousov-Zhabotinsky mixture filling catalyst-containing matrix and resulted gel's chemomechanical oscillations

We investigated phases and phase differences between coupled mechanical and chemical self-oscillations running in two kinds of newly synthesised chemomechanical gels. Processing of experimental data was model-free and it was based on spectral and wavelet approaches of the theory of dynamical systems. It was applied to samples of different sizes and compositions (Ru- and Fe-based gels). It was revealed that the Ru-based gels demonstrate a faster mechanical response to the redox changes of the Ru-moiety coupled to the Belousov-Zhabotinsky chemical reaction than the Fe-based gels. This demonstrated a significant phase difference between the redox changes of the Fe-moiety and the mechanical oscillations. Special attention was paid to the phase-coupling features for averaged higher harmonics, which are significant due to the high degree of nonlinearity of the chemomechanical oscillatory process.

Collective chemomechanical oscillations in active hydrogels

We report on the collective response of an assembly of chemomechanical Belousov-Zhabotinsky (BZ) hydrogel beads. We first demonstrate that a single isolated spherical BZ hydrogel bead with a radius below a critical value does not oscillate, whereas an assembly of the same BZ hydrogel beads presents chemical oscillation. A BZ chemical model with an additional flux of chemicals out of the BZ hydrogel captures the experimentally observed transition from oxidized nonoscillating to oscillating BZ hydrogels and shows this transition is due to a flux of inhibitors out of the BZ hydrogel. The model also captures the role of neighboring BZ hydrogel beads in decreasing the critical size for an assembly of BZ hydrogel beads to oscillate. We finally leverage the quorum sensing behavior of the collective to trigger their chemomechanical oscillation and discuss how this collective effect can be used to enhance the oscillatory strain of these active BZ hydrogels. These findings could help guide the eventual fabrication of a swarm of autonomous, communicating, and motile hydrogels.

Fe(bathophen)2(phen)-based self-oscillating gel driven by the Belousov–Zhabotinsky reaction

The synthesis of a new Fe(bathophen)2(phen)-based self-oscillating gel driven by the Belousov–Zhabotinsky reaction is described. The gel undergoes spontaneous chemomechanical oscillations without any on–off switching by external stimuli and demonstrates the dependence of chemomechanical behavior on the concentration of the catalyst in it.

Quenching of oscillations in a liquid metal via attenuated coupling.

In this work, we report a quenching of oscillations observed upon coupling two chemomechanical oscillators. Each one of these oscillators consists of a drop of liquid metal submerged in an oxidizing solution. These pseudoidentical oscillators have been shown to exhibit both periodic and aperiodic oscillatory behavior. In the experiments performed on these oscillators, we find that coupling two such oscillators via an attenuated resistive coupling leads the coupled system towards an oscillation quenched state. To further comprehend these experimental observations, we numerically explore and verify the presence of similar oscillation quenching in a model of coupled Hindmarsh-Rose (HR) systems. A linear stability analysis of this HR system reveals that attenuated coupling induces a change in eigenvalues of the relevant Jacobian, leading to stable quenched oscillation states. Additionally, the analysis yields a threshold of attenuation for oscillation quenching that is consistent with the value observed in numerics. So this phenomenon, demonstrated through experiments, as well as simulations and analysis of a model system, suggests a powerful natural mechanism that can potentially suppress periodic and aperiodic oscillations in coupled nonlinear systems.

Nanogel Crosslinking-Based Belousov-Zhabotinsky Self-Oscillating Polyacrylamide Gel with Improved Mechanical Properties and Fast Oscillatory Response.

The Belousov-Zhabotinsky (BZ) self-oscillating gel is a unique actuator suited for studying the behavior of intelligent soft robots. However, the traditional BZ self-oscillating polyacrylamide (PAAm) gel is easily broken and is slow to response to stimuli, which limits its practical application. Therefore, the preparation of BZ gels with sensitive responses to external stimuli and desirable, robust mechanical properties remains a challenge. In this work, PAAm-activated nanogels with unpolymerized double bonds are used as nanocrosslinkers to synthesize a nanogel crosslinking-based BZ (NCBZ) self-oscillating PAAm gel, whose mechanical properties, for example, antipuncture, cutting, and tensile properties, are superior to those of traditional PAAm BZ-self-oscillating gels. The oscillatory period of the traditional gel is much longer than that of the corresponding homogeneous BZ system, resulting from the slow response of the gel to changes in redox potential, whereas large, interconnected pores inside the NCBZ gel provide efficient channels for rapid species transport, supporting fast response of the gel, which results in almost the same period of chemomechanical oscillations as the homogeneous system under the same conditions. Scanning electron microscopy results show that the NCBZ gel is more stable than the traditional BZ PAAm gel after 7 h of oscillation. Our results make it possible to prepare robust gel motors and provide promising application prospects for smart soft robots, actuators, sensors, tissue engineering, and other applications.

Chemical Oscillation and Morphological Oscillation in Catalyst-Embedded Lyotropic Liquid Crystalline Gels.

Liquid crystalline gels offer promising means in generating smart materials due to programmable mechanics and reversible shape changes in response to external stimuli. We demonstrate a simple and convenient method of constructing catalyst-embedded lyotropic liquid crystalline (LLC) gels and achieve chemomechanical oscillator by converting chemical waves in Belousov–Zhabotinsky (BZ) reaction. We observe the directed chemical oscillations on LLC sticks accompanied by small-scale oscillatory swellings–shrinkages that are synchronized with the chemical waves of an LLC stick. To amplify the mechanical oscillations, we further fabricate small LLC fibers and achieve macroscopically oscillatory bending–unbending transition of the LLC fiber driven by a BZ reaction.

Synchronization of chemo-mechanical oscillators

The synchronization of chemically driven oscillators plays a crucial role in various biological motions. An artificial model system of these chemo-mechanical oscillators is proposed in this study. The oscillator is composed of three liquid layers (oil/water/oil), which exhibit a back and forth motion in a glass tube. This motion is caused by the chemical reaction between a water-soluble surfactant and oil-soluble anions. The frequency is unique for an individual experimental setup because it depends on the surface state of the glass sensitively. When the glass tube with the liquid oscillator is placed on a plate with mechanical vibration, the frequencies of the oscillator and mechanical vibration become similar within a certain frequency range of mechanical vibration. When two or more glass tubes are placed in a boat floating on a water surface, all frequencies agree with each other by the joggling motion of the boat. The entrainment into the external vibration and mutual synchronization on the boat are explained by a simple mathematical model. The proposed chemo-mechanical oscillator may be used as a primitive model system for studying the interplay of macroscopic motion and molecular scale processes that control chemically driven motion.

Episodic mineralising fluid injection through chemical shear zones

The nature of the geological mechanisms allowing mineralising fluids to flow from depth and form localized mineral deposits is uncertain and a matter of debate. Traditional assumptions of fluids travelling through highly permeable faults raise interesting questions about the existence of highly permeable faults at depths below the brittle-ductile transition, for example. A recent model of multi-physics oscillation can explain the behaviour of impermeable shear zones in such environments, under specific conditions where temperature sensitive endothermal reactions trigger in-situ release of fluids that lubricate the fault and lead to their reactivation. The response of such systems can be of various nature, including slow creep, one-off reactivation events, or episodic reactivation events during which the permeability increases by several orders of magnitudes and allows fluids from depth to flow upwards. In this contribution, we review briefly the previous studies on this chemo-mechanical oscillator and place the findings in the context of mineral exploration. We extend the parameter sensitivity analysis to the main two dimensionless parameters controlling the chemical reactions, the Arrhenius and Damkohler numbers, to understand how they affect the location of episodic slip instabilities in the global parameter space. We show that lower values of the Damkohler number reduce the range of Gruntfest values in which the oscillator operates and we propose some fitting relationships between the main parameters in various interesting areas of the parameter space.

On the possibility of spontaneous chemomechanical oscillations in adsorptive porous media.

We derive general conditions for the emergence of sustained chemomechanical oscillations from a non-oscillatory adsorption/desorption reaction in a gas/solid porous medium. The oscillations arise from the nonlinear response of the solid matrix to the loading of the adsorbed species. More particularly, we prove that, in order for oscillations to occur, adsorption of the gas must in general cause a swelling of the solid matrix. We also investigate the prototypical case of Langmuir kinetics both numerically and analytically.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.

Cessation of oscillations in a chemo-mechanical oscillator

In this paper, different methods for cessation of oscillations in a chemo-mechanical oscillator [mercury beating heart (MBH)] are presented. The first set of experiments were carried out on a single MBH oscillator. To achieve cessation of oscillations, two protocols, namely, inverted feedback and delayed feedback were employed. In the second set of experiments, two quasi-identical MBH oscillators are considered. They are first synchronized via a bidirectional attractive coupling. These two synchronized oscillators are thereafter coupled with a unidirectional repulsive coupling and the system dynamics were observed. Subsequently, in the next protocol, the effect of a unidirectional delay coupling on the two synchronized oscillators was explored. The cessation of oscillations in all the above experimental setups was observed as the feedback/coupling was switched on at a suitable strength. Oscillatory dynamics of the system were restored when the feedback/coupling was switched off.

Dependence of synchronization on frequency mismatch and network configuration in chemo-mechanical oscillators

In this paper, synchronization among the mercury beating heart (MBH) oscillators is studied. In the first set of experiments, two MBH oscillators were taken. Frequency of one oscillator is kept constant and that of the other is increased monotonically. These were then coupled using bidirectional and unidirectional coupling mechanisms separately. Dependence of synchronization on the frequency difference between the two oscillators is investigated. For the second set of experiments involving unidirectional coupling, an ensemble of fifteen oscillators was taken and different configurations of these oscillators were considered. These include an all-to-all network and fractionally distributed master slave configurations. The effect of both the extent of coupling and network configuration on synchronization among these oscillators was investigated.

Microfluidics Fabrication of Self-Oscillating Microgel Clusters with Tailored Temperature-Responsive Properties Using Polymersomes as "Microreactors".

Poly(N-isopropylacrylamide)-based microgel clusters were successfully prepared using polymersomes as "microreactors", which were fabricated through microfluidics. The clusters were formed from the cross-linking reaction between ruthenium/amino group dual functionalized poly(N-isopropylacrylamide) microgels and linear poly(N-isopropylacrylamide)-r-(N-acryloxysuccinimide)-based polymer linkers under neutral pH conditions. By simply adjusting the ratio of N-isopropylacrylamide to N-acryloxysuccinimide in the polymer cross-linkers, the internal structures of the clusters can be controlled; hence, the temperature response of the clusters can be regulated. It was demonstrated that these different microgel clusters showed various degrees of chemomechanical oscillations when the clusters were exposed to a catalyst-free solution containing Belousov-Zhabotinsky reaction substrates.

Experimental Evidence of Large Amplitude pH Mediated Autonomous Chemomechanical Oscillation.

Large amplitude autonomous chemomechanical oscillations were observed in a coupled system consisting of a porous pH-responsive hydrogel and a bromate-sulfite-manganese (II) pH oscillatory reaction. The porous structure effectively improves the chemomechanical response speed, and the negative feedback species of the bulk oscillation Mn2+ takes part in the coupling by forming complex and physical crosslinks with the responsive group in the gel. It strengthens the porous gel by forming additional networks, which may contribute to sustaining the long-lasting chemomechanical oscillation. Additionally, the interaction between Mn2+ and the hydrogel alters the period of the oscillatory reaction due to its binding competition with H+, the positive feedback species.

An oscillating dynamic model of collective cells in a monolayer

Periodic oscillations of collective cells occur in the morphogenesis and organogenesis of various tissues and organs. In this paper, an oscillating cytodynamic model is presented by integrating the chemomechanical interplay between the RhoA effector signaling pathway and cell deformation. We show that both an isolated cell and a cell aggregate can undergo spontaneous oscillations as a result of Hopf bifurcation, upon which the system evolves into a limit cycle of chemomechanical oscillations. The dynamic characteristics are tailored by the mechanical properties of cells (e.g., elasticity, contractility, and intercellular tension) and the chemical reactions involved in the RhoA effector signaling pathway. External forces are found to modulate the oscillation intensity of collective cells in the monolayer and to polarize their oscillations along the direction of external tension. The proposed cytodynamic model can recapitulate the prominent features of cell oscillations observed in a variety of experiments, including both isolated cells (e.g., spreading mouse embryonic fibroblasts, migrating amoeboid cells, and suspending 3T3 fibroblasts) and multicellular systems (e.g., Drosophila embryogenesis and oogenesis).

Partially synchronized states in an ensemble of chemo-mechanical oscillators

Partially synchronized (clustered) states are defined as coexisting coherent (synchronized) and incoherent (unsynchronized) domains in an ensemble of interacting oscillators. We report these clustered states in experiments involving an ensemble of sixteen mercury beating heart (MBH) oscillators. These oscillators interact via resistors and are subjected to two different network schemes: 1) All to all and 2) Nonlocal. For the all to all network, the coupling strengths were inhomogeneously distributed, whereas for the nonlocal network scenario, each oscillator was coupled, with an identical coupling strength, with four of its nearest neighbors in either direction. For both of these network schemes, partially synchronized states results into grouping of these oscillators, wherein some oscillators are synchronized and rest are unsynchronized. For all to all network, the partially synchronized states are observed, for the intermediate inhomogeneities, when subjected to the power law and the ‘U’ shape profiles of coupling strengths. Irrespective of the coupling profile chosen, low inhomogeneities in the coupling strengths leaves all the oscillators in a single coherent state whereas for the high inhomogeneities scenarios oscillators are located in the incoherent domain. In comparison, for the nonlocal network partially synchronized states emerge when the coupling constant is appropriately chosen. The experimental results for both these network scenarios have been analyzed using the redox time series (chemical activity) and the time evolution of the normalized areas for the mercury drop (mechanical activity). The existence of partially synchronized states in the experiments was verified using different diagnostic tools such as time series plot, space–time plot and average frequency.

Chemomechanical oscillations with a non-redox non-oscillatory reaction.

Periodic length changes, over 20%, were sustained in a pH-responsive gel by associating the methylene glycol-sulphite OH-producing clock-reaction with variations of the exchange time induced between the core of the gel and a steady chemical environment. This is the first synergistic actuator that operates beyond acid-producing redox reactions.

Long-range interactions, wobbles, and phase defects in chains of model cilia.

Eukaryotic cilia and flagella are chemo-mechanical oscillators capable of generating long-range coordinated motions known as metachronal waves. Pair synchronization is a fundamental requirement for these collective dynamics, but it is generally not sufficient for collective phase-locking, chiefly due to the effect of long-range interactions. Here we explore experimentally and numerically a minimal model for a ciliated surface: hydrodynamically coupled oscillators rotating above a no-slip plane. Increasing their distance from the wall profoundly affects the global dynamics, due to variations in hydrodynamic interaction range. The array undergoes a transition from a traveling wave to either a steady chevron pattern or one punctuated by periodic phase defects. Within the transition between these regimes the system displays behavior reminiscent of chimera states.

Synergistic Chemomechanical Oscillators: Periodic Gel Actuators without Oscillatory Chemical Reaction

SummarySynergistic chemomechanical oscillators fundamentally differ from BZ‐gels or ordinary pH‐actuators where oscillatory chemical reactions are required as (internal) “frequency generators”. Periodicity can arise from the interplay between a non‐periodic but nonlinear chemical reaction (e.g., a “pH‐switch”) and a geometrical feedback that modifies the transport time of species between the gel core and the environment. The experimental realization of several different such systems is essential to identify their universal properties. To be operational, the fine tuning of the gel's pH‐response to the region of the pH‐drop in a particular chemical reaction turned out to be an essential step. Simultaneously, the weak acid functional groups present in the gel modify the pH‐drop range, and this also needs to be considered. Analogous interdependence between chemical and physical actions is believed to be an underlying mechanism in primary biological processes.

Peristaltic waves in a responsive gel sustained by a halogen-free non-oscillatory chemical reaction

Formerly, we demonstrated in three chemical systems how the combination of the shrinking response of an appropriate responsive gel and a pH-switch type chemical reaction, which is not capable of oscillations by itself, can lead to self-oscillations in size and in pH in a piece of gel surrounded by a constant environment. We demonstrate that this can be realized at very mild chemical conditions: at ionic strength ∼0.015 M, with acid generated in concentrations ∼10 micromol/liter, and without halogen-containing oxidant. We discuss in detail how to adjust the gel-response to the chemical reaction for sustained motion. Travelling contraction wave trains along a long thin cylinder (Rsw < 0.50 mm) were sustained for more than 2 days. Considering the environmentally neutral reaction wastes, free from halogens or metal ions, biomaterials become attainable matrices in contrast to former chemomechanical oscillators which all operated under much harsher chemical conditions.