Dynamic Catalysis
Dynamic, or programmable, catalysis periodically oscillates the binding energies of adsorbates on a catalyst (for example by applied potential, strain, light or charge) so that different elementary steps are favored at different times in the cycle. The goal is a time-averaged turnover frequency above the Sabatier limit of any static catalyst. Modeling it requires predicting the cyclic steady state (limit cycle) reached under periodic forcing.
Analytical averages and limit cycles by multiple-scale perturbation (2025)
Colombo Tedesco and co-workers derived closed-form expressions for the time-averaged coverages and limit cycles of periodically forced surface reactions using a multiple time-scale expansion, valid when the forcing frequency is well above the fastest rate constant and the coverage swings are small. For a two-adsorbate scheme forced by a 0.1 eV, 1000 Hz square wave in binding energy, the analytical averages (0.3828 and 0.6172) and piecewise limit cycles matched boundary value problem simulations, while lower frequencies (3 Hz, the stepwise regime) or larger amplitudes (0.3 eV) degraded the limit cycle, though averages stayed within 0.04 (Colombo Tedesco et al. 2025). Summary: colombotedesco2025.