{ "node": { "id": "term:butler-volmer", "type": "Term", "label": "Butler–Volmer equation", "properties": { "id": "butler-volmer", "name": "Butler–Volmer equation", "section": "topic-electrochemistry", "definition": "The kinetic law relating current density at an electrode to its overpotential: current grows exponentially with overpotential in each direction. It is the charge-transfer term in every physics-based cell model.", "formula": "i = i₀[exp(α_a·Fη/RT) − exp(−α_c·Fη/RT)]", "related": [ "overpotential", "exchange-current-density", "charge-transfer", "newman-model" ], "example": { "title": "Compare equilibrium with a positive overpotential", "text": "For a symmetric one-electron example at 298.15 K, αa = αc = 0.5 and η = 25.7 mV give i/i₀ ≈ 1.04. 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Activation overpotential pays for charge transfer, concentration overpotential for depleted reactant, and both appear as polarization at the terminals.", "unit": "V", "related": [ "polarization", "butler-volmer", "exchange-current-density", "concentration-polarization" ], "url": "https://lemonergy.com/learn/glossary/overpotential/", "mentions": [ "electrode", "charge-transfer" ] } }, { "id": "term:exchange-current-density", "type": "Term", "label": "Exchange current density", "properties": { "id": "exchange-current-density", "name": "Exchange current density", "abbr": "i₀", "section": "topic-electrochemistry", "definition": "The equal and opposite current flowing each way across an electrode interface at equilibrium. 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Its resistance appears as a semicircle in impedance spectra and grows as films thicken and the cell cools.", "related": [ "butler-volmer", "double-layer", "electrochemical-impedance-spectroscopy", "overpotential", "solvation" ], "url": "https://lemonergy.com/learn/glossary/charge-transfer/", "mentions": [ "impedance", "electrode", "electrolyte" ] } }, { "id": "term:newman-model", "type": "Term", "label": "Newman model", "properties": { "id": "newman-model", "name": "Newman model", "abbr": "P2D", "aka": [ "pseudo-two-dimensional model", "Doyle–Fuller–Newman", "DFN" ], "section": "topic-transport", "definition": "The standard physics-based lithium-ion cell model: porous-electrode theory across the cell thickness, with solid diffusion solved in a representative spherical particle at every point — hence pseudo-two-dimensional. It predicts voltage from first principles but needs dozens of parameters.", "related": [ "porous-electrode-theory", "single-particle-model", "butler-volmer", "ficks-second-law", "parameterisation", "pybamm" ], "url": "https://lemonergy.com/learn/glossary/newman-model/", "mentions": [ "diffusion" ] } }, { "id": "term:electrode", "type": "Term", "label": "Electrode", "properties": { "id": "electrode", "name": "Electrode", "section": "topic-components", "definition": "A solid conductor where the cell’s reaction happens, in contact with the electrolyte. A lithium-ion cell has a negative electrode and a positive electrode, each a porous coating on a metal foil.", "related": [ "negative-electrode", "positive-electrode", "porous-electrode", "current-collector" ], "lesson": "fundamentals/cell-anatomy/#components", "example": { "title": "Two transport paths", "text": "Electrons need connected solid paths to the collector; ions need electrolyte paths to reaction sites. More of one constituent displaces others at fixed volume." }, "url": "https://lemonergy.com/learn/glossary/electrode/", "mentions": [ "electrolyte", "coating" ] } }, { "id": "visual:butler-volmer", "type": "Visual", "label": "Overpotential drives reaction current", "properties": { "title": "Overpotential drives reaction current", "summary": "At equilibrium, forward and reverse reaction currents cancel.", "readout": "At equilibrium net current is zero. At +50 mV, current density is 2.268 A/m².", "formula": "i = 2i₀ sinh(Fη / 2RT)", "note": "Fixed concentrations, symmetric transfer coefficients and no transport limitation.", "software": { "status": "reference", "label": "Reference concept", "body": "This symmetric Butler–Volmer relation assumes one electron, α = 0.5 and 25 °C. It is a reference equation, not an implemented reaction model in battery-core.", "href": "../chapter-1/" }, "html": "
Symmetric reaction kinetics at 25 °C
Symmetric reaction kinetics at 25 °COverpotential (V) versus Current density (A/m²). Net reaction current. Interpretation follows the graphs.-18.5-0.15-9.24-0.075009.240.07518.50.15Overpotential (V)Current density (A/m²)
Net reaction current
" } } ] }