Quadratic response of a chemical reaction to external oscillations

Abstract

We develop a second-order response theory to investigate the effects of external periodic perturbations on a chemical reaction at a stable steady state in an open reactor. We apply the theory to the quadratic Schlögl model, a single-variable nonlinear reaction. In the presence of oscillating reactant or product concentrations or oscillating rate coefficients, the average intermediate concentration, the fluxes, and the dissipation are each a Lorentzian function of frequency with midpoint at the inverse relaxation time of the system. Thus even very short relaxation times can be determined by measuring average rates as a function of frequency of the perturbation. The amplitude of the Lorentzian depends on the chemical mechanism of the reaction and is proportional to the square of the amplitude of the applied perturbation. We also show that energy from the perturbation can be used to drive the reaction in a direction opposite of that predicted by the Gibb’s free energy difference of reactants and products, even under circumstances where the overall affinity is independent of the perturbation.