{ "node": { "id": "term:activation-energy", "type": "Term", "label": "Activation energy", "properties": { "id": "activation-energy", "name": "Activation energy", "abbr": "Eₐ", "section": "topic-aging", "definition": "The energy barrier a reaction must cross, which sets how sensitive its rate is to temperature in the Arrhenius law. Fitted values for lithium-ion aging are typically 20–60 kJ/mol, and they differ for each mechanism.", "unit": "kJ/mol", "related": [ "arrhenius", "calendar-aging", "accelerated-aging" ], "url": "https://lemonergy.com/learn/glossary/activation-energy/", "mentions": [] } }, "edges": [ { "id": "edge:18", "source": "term:activation-energy", "target": "workflow:arrhenius", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:1594", "source": "term:activation-energy", "target": "topic:topic-aging", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:1595", "source": "term:activation-energy", "target": "term:arrhenius", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1596", "source": "term:activation-energy", "target": "term:calendar-aging", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1597", "source": "term:activation-energy", "target": "term:accelerated-aging", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:1598", "source": "term:activation-energy", "target": "visual:arrhenius", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:1599", "source": "term:activation-energy", "target": "reference:iupac-arrhenius", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "workflow:arrhenius", "type": "Workflow", "label": "Compare reaction rates", "properties": { "id": "arrhenius", "title": "Compare reaction rates", "kind": "core", "summary": "Lemonergy Core evaluates this relation.", "steps": [ "Open the lesson and inspect the equation.", "Change one input while holding the others fixed." ], "example": "At an illustrative 50 kJ/mol activation energy, raising temperature from 25 °C to 35 °C gives a rate factor about 1.92.", "observe": "Compare the result with the equation and units.", "limits": "This factor alone does not predict lifetime or capacity loss.", "url": "https://lemonergy.com/learn/fundamentals/battery-aging/#arrhenius", "label": "Open the worked lesson", "evidence": [ "src/battery_core/aging.py" ] } }, { "id": "topic:topic-aging", "type": "Topic", "label": "Aging and degradation", "properties": { "id": "topic-aging", "name": "Aging and degradation", "lede": "Why a cell loses capacity and gains resistance, and the mechanisms behind it.", "context": "Separate mechanisms, observations and fitted models.", "example": "Capacity loss and resistance rise can have different causes; a film-growth curve cannot identify both.", "lesson_url": "https://lemonergy.com/learn/fundamentals/battery-aging/", "lesson_label": "Open aging" } }, { "id": "term:arrhenius", "type": "Term", "label": "Arrhenius law", "properties": { "id": "arrhenius", "name": "Arrhenius law", "section": "topic-aging", "definition": "The rule that a rate constant is proportional to exp(−Ea/RT), so a thermally activated reaction speeds up steeply with temperature. Near room temperature many degradation reactions roughly double their rate for every +10 °C.", "formula": "k = A·exp(−Eₐ/RT)", "related": [ "activation-energy", "calendar-aging", "operating-temperature", "accelerated-aging", "celsius-kelvin" ], "lesson": "fundamentals/battery-aging/#arrhenius", "example": { "title": "Compare reaction-rate factors", "text": "For an illustrative activation energy of 40 kJ/mol, increasing temperature from 25 °C to 35 °C multiplies the modeled rate by about 1.69. Convert both temperatures to kelvin before evaluating the exponential." }, "notes": [ "A reaction-rate factor alone is not a prediction of battery lifetime." ], "url": "https://lemonergy.com/learn/glossary/arrhenius/", "mentions": [] } }, { "id": "term:calendar-aging", "type": "Term", "label": "Calendar aging", "properties": { "id": "calendar-aging", "name": "Calendar aging", "section": "topic-aging", "definition": "Degradation that happens with time even when a cell is not cycled — in storage, for example. It is driven mainly by side reactions such as SEI growth and accelerates with temperature.", "related": [ "cycle-aging", "sei", "arrhenius", "square-root-of-time", "calendar-life" ], "lesson": "fundamentals/battery-aging/#whole-cell", "url": "https://lemonergy.com/learn/glossary/calendar-aging/", "mentions": [] } }, { "id": "term:accelerated-aging", "type": "Term", "label": "Accelerated aging test", "properties": { "id": "accelerated-aging", "name": "Accelerated aging test", "section": "topic-testing", "definition": "Aging cells faster than in service — at higher temperature, higher SOC or higher rate — and extrapolating to real conditions with a model such as Arrhenius. The extrapolation only holds if acceleration does not change which mechanism dominates.", "related": [ "arrhenius", "calendar-aging", "cycle-aging", "aging-model", "reference-performance-test" ], "url": "https://lemonergy.com/learn/glossary/accelerated-aging/", "mentions": [ "state-of-charge" ] } }, { "id": "visual:arrhenius", "type": "Visual", "label": "Temperature and reaction rate", "properties": { "title": "Temperature and reaction rate", "summary": "Compare an activated process with its rate at 25 °C.", "readout": "At 25 °C: 1×. At 35 °C: 1.924×. At 45 °C: 3.554×.", "formula": "k(T)/k(T_ref) = exp[(Eₐ/R)(1/T_ref − 1/T)]", "note": "The equation uses kelvin. One activated process is represented, not lifetime.", "software": { "status": "implemented", "label": "Implemented in battery-core", "body": "arrhenius_factor returns a rate multiplier from temperature and activation energy. It does not predict cell lifetime.", "href": "../fundamentals/battery-aging/" }, "html": "
Relative reaction rate
Relative reaction rateTemperature (°C) versus Rate multiplier (×). Relative to 25 °C. Interpretation follows the graphs.002.18154.37306.55458.7460Temperature (°C)Rate multiplier (×)
Relative to 25 °C
" } }, { "id": "reference:iupac-arrhenius", "type": "Reference", "label": "Arrhenius equation", "properties": { "title": "Arrhenius equation", "publisher": "IUPAC Gold Book", "url": "https://goldbook.iupac.org/terms/view/A00446", "type": "Terminology reference", "scope": "Temperature dependence of reaction-rate constants and the assumptions about activation energy.", "year": 2025, "accessed": "2026-10-27" } } ] }