Electrocatalysis — catalysis of faradaic reactions at electrode / electrolyte interfaces. Foundations: (1) Butler-Volmer current-overpotential law (Butler 1924; Erdey-Grúz & Volmer 1930): j = j₀·(exp(αfη) - exp(-(1-α)fη)) where f =…
electrocatalysis
Butler-Volmer: j = j₀·(exp(αfη) - exp(-(1-α)fη))
Butler-Volmer equation (Butler 1924; Erdey-Grúz & Volmer 1930) — the foundational current-overpotential law of electron-transfer…
Tafel slope b = 2.303·RT/(αF); mechanistic fingerprint
Tafel slope b (Tafel 1905) is the d η / d log|j| derivative of the Butler-Volmer equation in the high-overpotential regime — the slope of η…
Sabatier volcano: log(j₀) peaks at ΔG_bind ≈ 0
Sabatier principle (Sabatier 1911) — catalysts bind intermediates 'just right': too weakly and activation of the bond is insufficient; too…
BV anchors: j(η=0)=0; linear regime j ≈ j₀·f·η (sp.series O(η²))
Sympy-exact witness of the Butler-Volmer zero-overpotential identity and the linear regime via Taylor expansion. Setup: j = j_0·(exp(αfη)…
Tafel 25°C α=1/2: b = 1426462079/12060625000 V ≈ 118.27 mV/dec
Sympy-exact witness of the Tafel slope at the canonical textbook anchor T = 298 K, α = 1/2. Setup: b = 2.303·R·T/(α·F) as a sympy Rational…
Nernst: E(Q=1)=E°; ΔE(10×,298K,n=1) = -619393·log(10)/24121250 V
Sympy-exact witness of the Nernst equation standard-state identity and the per-decade potential shift at 25 °C. Setup: E = E_0 -…