Each cycle charges a fresh batch of substrate into the vessel with the surviving organocatalyst. Substrate converts to product by first-order kinetics with an effective rate that scales with how much active catalyst is left:
k_eff = k₀ · (N_active / N₀)
Conversion: X(t) = 1 − e^(−k_eff·t)
Turnover number: TON = Σ (moles product) / N₀
Every molecule of substrate is assigned a random first-order waiting time t_i = −ln(1−u)/k_eff (u uniform on [0,1)) — the same statistics that produce the macroscopic exponential conversion curve above, so the visible per-particle color flips reproduce X(t) exactly on average. The bottom-right panel plots that theoretical curve live against the batch's own realized fraction converted, so you can see the stochastic scatter settle onto the smooth exponential as the cycle runs.
- Initial catalyst loading — how many catalyst particles are charged into the very first batch (sets N₀, the turnover-number denominator).
- Rate constant k₀ — intrinsic activity of the catalyst when it is fully fresh (N_active = N₀).
- Leaching loss — the fraction of the still-active catalyst that dissolves into solution and is lost (not recoverable) at the end of every cycle: N_active ← N_active·(1 − L).
- Run Next Cycle — animates one fixed-duration batch reaction, then applies leaching and updates the cumulative TON.
- Drag inside the vessel panel to pan the view, scroll/pinch to zoom — useful once the catalyst dust thins out and you want a closer look.
Real-world relevance: this is exactly why industrial organocatalysis reports turnover number alongside yield — a catalyst that gives 95% yield once but leaches 15% of its mass every reuse is worth far less than one giving 80% yield across ten clean cycles. Immobilizing the catalyst on a solid support is the usual fix, trading a lower initial activity for a much lower leaching rate.