Dynamic model of self-oscillating gels and the controllability analysis

Self-oscillating gels, i.e., BZ gels, are a typical branch of soft smart materials with a large periodic deformation of shrinking and swelling driven by the Belousov-Zhabotinsky chemical reaction (BZ reaction). BZ gels could be widely applied in the fields of actuators, sensors, drug release and bionic system. Based on the Oregonator model of the BZ reaction and the mechanical equilibrium of the gel deformation, a simplified dynamic model, only consisting of a second order differential equation, is given to reformulate the complicated process of the oscillatory deformation. It is demonstrated that the phase space trajectory of BZ gels presents a limit-cycle oscillation (i.e., steady-state periodic oscillation). Subsequently, the periodic solution of oscillation is obtained by adopting an improved shooting method and the influence of some adjustable system parameters on the mechanical characters of the oscillatory deformation (i.e., pattern, period, amplitude) is systematically investigated, where the system parameters are dependent on the concentration of reactants, catalyst e_ciency and hydrophobicity of polymers. The conclusion demonstrates that the system maintains a limit-cycle oscillation in the case of certain selected values of the system parameters and the mechanical characters of the system appear predictable changes while the parameters are changed. This study theoretically supports the controllability of self-oscillating gels and their potential applications.