Energy and power characteristics of nanocatalyzed Belousov-Zhabotinsky reactions via bifurcation analyses

Abstract

Active stimuli-responsive materials, intrinsically powered by chemical reactions, have immense capabilities that can be harnessed for designing synthetic systems for a variety of biomimetic applications. It goes without saying that the key aspect involved in the designing of such systems is to accurately estimate the amount of energy and power available for transduction through various mechanisms. Belousov-Zhabotinsky (BZ) reactions are dynamical systems, which exhibit self-sustained nonlinear chemical oscillations, as their catalyst undergoes periodic redox cycles in the presence of reagents. The unique feature of BZ reaction based active systems is that they can continuously perform mechanical work by transducing energy from sustained chemical oscillations. The objective of our work is to use bifurcation analyses to identify oscillatory regimes and quantify energy-power characteristics of the BZ reaction based on nanocatalyst activity and BZ reaction formulations. Our approach involves not only the computation of higher order Lyapunov and frequency coefficients but also Hamiltonian functions, through normal form reduction of the kinetic model of the BZ reaction. Ultimately, using these calculations, we determine amplitude, frequency, and energy-power densities, as a function of the nanocatalysts’ activity and BZ formulations. As normal form representations are applicable to any dynamical system, we believe that our framework can be extended to other self-sustained active systems, including systems based on stimuli-responsive materials.