Harmonic resonance and entrainment of propagating chemical waves by external mechanical stimulation in BZ self-oscillating hydrogels.

Smart polymer materials that are nonliving yet exhibit complex "life-like" or biomimetic behaviors have been the focus of intensive research over the past decades, in the quest to broaden our understanding of how living systems function under nonequilibrium conditions. Identification of how chemical and mechanical coupling can generate resonance and entrainment with other cells or external environment is an important research question. We prepared Belousov-Zhabotinsky (BZ) self-oscillating hydrogels which convert chemical energy to mechanical oscillation. By cyclically applying external mechanical stimulation to the BZ hydrogels, we found that when the oscillation of a gel sample entered into harmonic resonance with the applied oscillation during stimulation, the system kept a "memory" of the resonant oscillation period and maintained it post stimulation, demonstrating an entrainment effect. More surprisingly, by systematically varying the cycle length of the external stimulation, we revealed the discrete nature of the stimulation-induced resonance and entrainment behaviors in chemical oscillations of BZ hydrogels, i.e., the hydrogels slow down their oscillation periods to the harmonics of the cycle length of the external mechanical stimulation. Our theoretical model calculations suggest the important roles of the delayed mechanical response caused by reactant diffusion and solvent migration in affecting the chemomechanical coupling in active hydrogels and consequently synchronizing their chemical oscillations with external mechanical oscillations.

Delayed Mechanical Response to Chemical Kinetics in Self-Oscillating Hydrogels Driven by the Belousov-Zhabotinsky Reaction.

We show experimentally that chemical and mechanical self-oscillations in Belousov-Zhabotinsky hydrogels are inherently asynchronous, that is, there is a detectable delay in swelling-deswelling response after a change in the chemical redox state. This phenomenon is observable in many previous experimental studies and potentially has far-reaching implications for the functionality and response time of the material in future applications; however, so far, it has not been quantified or reported systematically. Here, we provide a comprehensive qualitative and quantitative description of the chemical-to-mechanical delay, and we propose to explain it as a consequence of the slow nonequilibrium swelling-deswelling dynamics of the polymer material. Specifically, standard hydrogel pieces are large enough that transport processes, for example, counterion migration and water diffusion, cannot occur instantaneously throughout the entire gel piece, as opposed to previous theoretical considerations. As a result, the volume response of the polymer to a chemical change may be governed by a characteristic response time, which leads to the emergence of delay in mechanical oscillation. This is supported by our theoretical calculations.

Reaction fronts of the autocatalytic hydrogenase reaction.

We have built a model to describe the hydrogenase catalyzed, autocatalytic, reversible hydrogen oxidation reaction where one of the enzyme forms is the autocatalyst. The model not only reproduces the experimentally observed front properties, but also explains the found hydrogen ion dependence. Furthermore, by linear stability analysis, two different front types are found in good agreement with the experiments.

Determination of the diffusion coefficient of hydrogen ion in hydrogels.

The role of diffusion in chemical pattern formation has been widely studied due to the great diversity of patterns emerging in reaction-diffusion systems, particularly in H+-autocatalytic reactions where hydrogels are applied to avoid convection. A custom-made conductometric cell is designed to measure the effective diffusion coefficient of a pair of strong electrolytes containing sodium ions or hydrogen ions with a common anion. This together with the individual diffusion coefficient for sodium ions, obtained from PFGSE-NMR spectroscopy, allows the determination of the diffusion coefficient of hydrogen ions in hydrogels. Numerical calculations are also performed to study the behavior of a diffusion-migration model describing ionic diffusion in our system. The method we present for one particular case may be extended for various hydrogels and diffusing ions (such as hydroxide) which are relevant e.g. for the development of pH-regulated self-healing mechanisms and hydrogels used for drug delivery.