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 farreaching 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-tomechanical 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.