# 循环伏安法模拟器

交互式三维电化学：三角波电位扫描、Butler-Volmer 动力学、Randles-Sevcik 分析与 EC 机理诊断。

> 标准页面: https://elysiatools.com/zh/visualizations/cyclic-voltammetry

- **分类:** Chemistry

## 概述

Interactive electroanalytical chemistry — distinct from the existing galvanic-cell / concentration-cell / electrolytic-cell / battery-principles / redox-titration cases (equilibrium thermodynamics and cell diagrams, not voltammetric transients); this is the only case simulating the dynamic current response of a triangle-wave potential sweep, the workhorse technique of battery, sensor and electrocatalysis research. The model performs a live digital simulation (no precomputed curves) of Fick's second law ∂C/∂t = D ∂²C/∂x² on a semi-infinite finite-difference grid using the Feldberg box method (λ = DΔt/Δx² = 0.45, grid auto-scales with scan rate so accuracy is uniform from 0.01 to 1000 V/s), coupled at the electrode plane to Butler–Volmer heterogeneous kinetics k_f = k⁰e^(−αfη), k_b = k⁰e^((1−α)fη) via a half-interval flux-conservation boundary that converges exactly to the Nernst condition as k⁰ → ∞ (verified against the Cottrell limit to <0.1% and Randles–Ševčík to ~0.2% at the first-cycle peak). An EC mechanism (irreversible follow-up reaction R → Z with rate k_c, exact exponential propagator) demonstrates coupled-chemistry diagnostics. Peak analysis includes the Nicholson baseline correction: the anodic peak is re-measured against the √t-extrapolated cathodic tail, recovering |i_pa/i_pc| = 1.000 for the reversible couple (the zero-baseline ratio ~0.79 is also reported, teaching why baseline correction matters). Analytics: reversible Randles–Ševčík i_p = 2.69×10⁵·n^3/2·A·D^1/2·C·v^1/2, irreversible 2.99×10⁵·n·(αn_a)^1/2, Nicholson ψ = k⁰/√(πDfv) with the full ψ→ΔEp working curve (61 mV at ψ=20 … 212 mV at ψ=0.1) and its inversion k⁰ = ψ·√(πDfv) for real-time rate-constant estimation, plus the EC zone parameter K = k_c·t½. Four visualization panels: (1) The i–E voltammogram (the classic duck) with the forward cathodic sweep in cyan and reverse anodic in gold, E⁰′ reference line, peak markers with dotted drop-lines, animated scan replay drawing the curve sweep-by-sweep with a moving potential marker. (2) A rotatable 3D E–t–i trace showing the triangle-wave potential as a grey zigzag in the i=0 plane with the current response as a colour-coded ribbon connected by depth stems — multiple cycles braid into loops. (3) Concentration profiles of O and R vs distance from the electrode with the diffusion-layer thickness δ ≈ √(πDt) marked, animating through ~24 stored snapshots during scan replay. (4) Scan-rate diagnostic |i_pc| vs √v: the simulation is re-run at seven log-spaced scan rates (0.01–1000 V/s) and plotted against the analytic Randles–Ševčík line — diffusion control stays linear, fast-scan kinetics bend it down, and EC catalysis bends it up at slow scans. Adjustable parameters: scan rate v (0.01–1000 V/s, log), diffusion coefficient D (3×10⁻⁷–10⁻⁴ cm²/s, log), bulk concentration C (0.05–20 mM), transfer coefficient α (0.2–0.8), standard rate constant k⁰ (10⁻⁶–30 cm/s, log), EC follow-up rate k_c (0–200 s⁻¹), and cycles (1–4). Five mechanism presets: Reversible (ferrocene-like k⁰=1), Quasi-reversible (ψ≈1, ΔEp≈81 mV), Irreversible (k⁰=10⁻⁴, ΔEp≈448 mV), EC mechanism (k_c=25, K≈112, anodic peak vanishes + catalytic enhancement), and Fast-scan diagnostic (100 V/s — a reversible couple turns quasi-reversible before your eyes). Real-time diagnostics: regime badge (reversible/quasi/irreversible), ψ, ΔEp, i_pc, i_pa, zero-baseline and baseline-corrected |i_pa/i_pc|, k⁰ estimated from ΔEp, analytic Randles–Ševčík i_p, diffusion-layer thickness δ, and EC parameter K. Educational content covers the triangle-wave experiment and the duck anatomy, the finite-difference box method and Butler–Volmer boundary, the Randles–Ševčík equation and √v test, Nicholson ψ and measuring k⁰ from ΔEp, and EC mechanism diagnosis via scan-rate gating (the three pillars of mechanistic voltammetry). Multi-language support (zh, en, es, fr, de, ru, pt).

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