Catalyst Volcano Plot (2D): Kinetic Monte Carlo Sabatier Explorer

Catalyst Descriptor

Binding energy ΔE -1.20 eV

Conditions

Temperature T 550 K

Scaling-relation slope γ 0.70

Kinetic Monte Carlo (live)

Analytic TOF (viz units)

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Measured flux (KMC)

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Convergence error

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Simulated site-seconds

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Occupancy θ (analytic)

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Occupancy (measured)

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Rate-limiting regime

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How it works

This is the same Sabatier-principle chemistry as the 3D version of this simulator, verified here by an independent computational method: a kinetic Monte Carlo (KMC) simulation of many separate lattice sites, rather than a scripted animation.

E₁(ΔE) = E₁⁰ + γ·ΔE     E₂(ΔE) = E₂⁰ − γ·ΔE      (BEP scaling)
rᵢ = Aᵢ·exp(−Eᵢ / kB·T)                          (Arrhenius rates)
each site: EMPTY --r₁--> BOUND --r₂--> EMPTY      (independent 2-state Markov chain)
closed form (harmonic mean): TOF = r₁·r₂ / (r₁+r₂)

Every one of the 22×22 squares on the left is an independent site with its own random clock: each frame it flips EMPTY→BOUND with probability 1−e^(−r₁·dt), or BOUND→EMPTY (a real "turnover", counted) with probability 1−e^(−r₂·dt) — an exact discrete-time realization of a continuous-time Markov chain, not a pre-scripted cadence. Turnovers are tallied since the last parameter change and divided by (sites × elapsed time) to get a measured flux, which is plotted live against the closed-form harmonic-mean formula. The two should converge as more site-seconds accumulate — exactly the statistical-mechanics argument for why the harmonic-mean formula is correct in the first place (steady-state flux through two rate-limited states in series).

Raw rates span many orders of magnitude across the slider range, so both r₁ and r₂ are rescaled by the same live factor K = 3 / max(r₁,r₂) before the KMC runs — this preserves their ratio (so θ = r₁/(r₁+r₂) and the volcano's peak location are untouched) while keeping the faster channel at a watchable ~3 events/sec. Far from the peak, one channel is genuinely negligible on human timescales — the lattice will show almost no turnovers, which is itself the correct physics of a starved or poisoned catalyst, not a stall.

ΔE slider / preset metals — same illustrative descriptor axis as the 3D version.
Temperature / scaling slope γ — reshape both barriers exactly as before; changing either resets the KMC measurement window so it re-converges cleanly for the new regime.
Convergence error — |measured − analytic| / analytic, only shown once enough turnovers have been sampled to be meaningful; it should shrink as the "simulated site-seconds" counter grows.

22 × 22 independent KMC sites Turnovers accumulate since last reset

Empty site Bound site Volcano curve (analytic) Measured KMC flux