{ "node": { "id": "term:bruggeman-relation", "type": "Term", "label": "Bruggeman relation", "properties": { "id": "bruggeman-relation", "name": "Bruggeman relation", "section": "topic-transport", "definition": "The common estimate of effective transport in a porous layer: multiply the bulk conductivity or diffusivity by porosity to the power 1.5. Real electrodes often deviate, so measured tortuosity is preferred when available.", "formula": "D_eff = D · ε^1.5", "related": [ "tortuosity", "porosity", "porous-electrode-theory" ], "example": { "title": "Estimate an effective diffusivity", "text": "Using the illustrative relation D_eff = D ε^1.5 with porosity ε = 0.4 gives D_eff ≈ 0.253D. This empirical geometry approximation does not replace a measured tortuosity." }, "url": "https://lemonergy.com/learn/glossary/bruggeman-relation/", "mentions": [ "diffusion-coefficient" ] } }, "edges": [ { "id": "edge:2100", "source": "term:bruggeman-relation", "target": "topic:topic-transport", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:2101", "source": "term:bruggeman-relation", "target": "term:tortuosity", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2102", "source": "term:bruggeman-relation", "target": "term:porosity", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2103", "source": "term:bruggeman-relation", "target": "term:porous-electrode-theory", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/bruggeman-relation/diffusion-coefficient", "source": "term:bruggeman-relation", "target": "term:diffusion-coefficient", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:2105", "source": "term:bruggeman-relation", "target": "visual:porous", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:2106", "source": "term:bruggeman-relation", "target": "reference:doyle-model", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "topic:topic-transport", "type": "Topic", "label": "Transport and modelling", "properties": { "id": "topic-transport", "name": "Transport and modelling", "lede": "How ions move, and the equations and models that describe a cell.", "context": "Specify phase, direction and boundaries.", "example": "The same concentration difference across 10 μm gives ten times the gradient across 100 μm; at equal D, first-law flux magnitude is ten times greater.", "lesson_url": "https://lemonergy.com/learn/transport/ficks-first-law/", "lesson_label": "Open diffusion" } }, { "id": "term:tortuosity", "type": "Term", "label": "Tortuosity", "properties": { "id": "tortuosity", "name": "Tortuosity", "abbr": "τ", "section": "topic-transport", "definition": "How winding the path through a porous layer is, compared with a straight line through it. High tortuosity means ions travel much further than the layer is thick, which limits how fast a thick, dense electrode can be charged or discharged.", "unit": "—", "related": [ "porosity", "bruggeman-relation", "porous-electrode", "rate-capability", "ionic-path" ], "lesson": "fundamentals/cell-architecture/#porosity", "url": "https://lemonergy.com/learn/glossary/tortuosity/", "mentions": [ "electrode", "winding" ] } }, { "id": "term:porosity", "type": "Term", "label": "Porosity", "properties": { "id": "porosity", "name": "Porosity", "abbr": "ε", "section": "topic-components", "definition": "The fraction of a layer’s volume that is empty space. In a lithium-ion electrode the pores — roughly 20–35 % of the volume after calendering — are filled with electrolyte, which carries ions to the particles.", "unit": "—", "related": [ "porous-electrode", "tortuosity", "calendering", "bruggeman-relation" ], "lesson": "fundamentals/cell-architecture/#porosity", "example": { "title": "Use the volume basis", "text": "Pore volume of 0.3 cm³ within 1 cm³ total electrode volume means 30% porosity. It does not specify connectivity or tortuosity." }, "url": "https://lemonergy.com/learn/glossary/porosity/", "mentions": [ "electrode", "electrolyte" ] } }, { "id": "term:porous-electrode-theory", "type": "Term", "label": "Porous-electrode theory", "properties": { "id": "porous-electrode-theory", "name": "Porous-electrode theory", "section": "topic-transport", "definition": "The framework, due to Newman and co-workers, that treats a porous electrode as two overlapping continua — solid and electrolyte — exchanging current everywhere through their shared surface. It underlies every physics-based lithium-ion model.", "related": [ "newman-model", "porous-electrode", "bruggeman-relation", "butler-volmer" ], "url": "https://lemonergy.com/learn/glossary/porous-electrode-theory/", "mentions": [ "electrode", "electrolyte" ] } }, { "id": "term:diffusion-coefficient", "type": "Term", "label": "Diffusion coefficient", "properties": { "id": "diffusion-coefficient", "name": "Diffusion coefficient", "abbr": "D", "aka": [ "diffusivity" ], "section": "topic-transport", "definition": "The proportionality constant D in Fick’s first law, in m²/s. It sets how fast a species spreads for a given concentration gradient.", "unit": "m²/s", "related": [ "ficks-first-law", "solid-state-diffusion", "gitt", "diffusion" ], "lesson": "transport/ficks-first-law/#law", "url": "https://lemonergy.com/learn/glossary/diffusion-coefficient/", "mentions": [ "concentration-gradient" ] } }, { "id": "visual:porous", "type": "Visual", "label": "Porosity reduces effective transport", "properties": { "title": "Porosity reduces effective transport", "summary": "A Bruggeman relation approximates transport through a porous medium.", "readout": "At 40% porosity, D_eff is 25.298% of bulk diffusivity.", "formula": "D_eff = D εᵇ", "note": "An empirical pore-structure assumption; actual tortuosity must be characterized.", "software": { "status": "reference", "label": "Reference concept", "body": "The flux helper accepts a supplied diffusivity. It does not estimate porosity or tortuosity. The shown D_eff = D εᵇ relationship is an explicit teaching assumption.", "href": "../transport/ficks-first-law/" }, "html": "
Effective diffusivity fraction
Effective diffusivity fractionPorosity ε (fraction) versus D_eff / D (fraction). εᵇ; Straight-pore scaling ε. Interpretation follows the graphs.000.250.250.50.50.750.7511Porosity ε (fraction)D_eff / D (fraction)
εᵇStraight-pore scaling ε (dashed)
" } }, { "id": "reference:doyle-model", "type": "Reference", "label": "Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell", "properties": { "title": "Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell", "publisher": "Journal of The Electrochemical Society", "url": "https://doi.org/10.1149/1.2221597", "type": "Research article", "scope": "Porous-electrode transport and insertion-cell modeling; foundational work rather than a specification for a particular commercial cell.", "year": 1993, "authors": [ "Marc Doyle", "Thomas F. Fuller", "John Newman" ], "accessed": "2026-10-27" } } ] }