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.
Limit-cycle simulation and waveform optimization (2024)
Tedesco, Kitchin and Laird computed the cyclic steady state of a unimolecular programmable catalyst directly, as a boundary value problem with periodicity constraints solved in Pyomo with IPOPT, which avoided integrating many cycles and was orders of magnitude faster than forward integration at high frequencies (Tedesco et al. 2024). Wrapping this simulation in optimizers over square, sine, triangle, sawtooth, smoothed square and Gaussian-pulse waveforms showed that duty cycle and offset matter as much as frequency and amplitude; the best square wave (1500 Hz, 0.40 eV amplitude, 1.37 eV offset, duty cycle 0.78) reached a time-averaged TOF of 853 s-1, about 1.7 x 104 times the static Sabatier-peak rate of 0.05 s-1. Summary: tedesco2024.
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.