The Unbound Mean Field model of Catalysis

A free research tool from Aalborg University and the CAPeX Pioneer Center that computes the three classical kinetic descriptors — apparent reaction order (γ_m), Tafel slope (b), and apparent activation energy (E_app) — for arbitrary heterogeneous and electrocatalytic reaction networks, from a single domain-independent kinetic matrix 𝒦. All three observables are realisations of the same algebraic object, γ_ξ = d ln r_net / dξ, evaluated on the perturbation variable ξ of each domain (concentration, electrode potential, temperature).

Loading the interactive app… If this notice does not disappear within a few seconds, JavaScript is disabled or your client does not execute it. The same content is available in static form at the links below — none of them require JavaScript.

Read the theory

How does it work? — the full derivation in plain markdown with the math preserved as LaTeX (mirrors the in-app How does it work? panel).
/llms.txt — a concise machine-readable summary of the app, the API, and the citations, following the llms.txt convention.

Use the API

/docs — interactive Swagger UI for the JSON HTTP API (/api/parse, /api/analyze, /api/regimes-match, …).
/openapi.json — the OpenAPI schema (machine-readable, suitable for code generation or MCP integration).
/api/version — current backend app_version and prompt_version.

Minimal API call

The same computation the in-browser app does, in one HTTP POST. No auth, CORS-open, JSON in / JSON out.

curl -X POST https://reactionorders.energy.aau.dk/api/analyze \
  -H 'Content-Type: application/json' \
  -d '{
    "equations": "H+ + e- <=> *H\n2 *H <=> H2",
    "chi":   [1.0, 0.0],
    "beta":  [0.5, 0.5],
    "Psi":   [[0.0]],
    "T_ref": 298.15
  }'

Returns the apparent reaction orders, Tafel slope (mV/decade), and apparent activation energy (kJ/mol) for the given mechanism. Full endpoint catalogue at /llms.txt.

Cite this work

Brandes, B. A. & Vegge, T., On the Universal Algebraic Structure of Kinetic Observables in Catalysis, 2026 (in preparation).
Brandes, B. A., Hansen, H. A., Vegge, T. & Chatzichristodoulou, C., Correcting the Foundations of Tafel Analysis in Electrocatalysis, 2026 (in submission).