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      "id": "tortuosity",
      "name": "Tortuosity",
      "abbr": "τ",
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      "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": "—",
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        "meaning": "Related context; not a causal claim"
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      "id": "edge:mentions/tortuosity/electrode",
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      "id": "topic:topic-transport",
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      "label": "Transport and modelling",
      "properties": {
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        "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"
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    {
      "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": [
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          "tortuosity",
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          "bruggeman-relation"
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          "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."
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        "url": "https://lemonergy.com/learn/glossary/porosity/",
        "mentions": [
          "electrode",
          "electrolyte"
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      "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"
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      "id": "term:porous-electrode",
      "type": "Term",
      "label": "Porous electrode",
      "properties": {
        "id": "porous-electrode",
        "name": "Porous electrode",
        "section": "topic-components",
        "definition": "An electrode made of active-material particles, conductive additive and binder with electrolyte-filled pores between them. Its large internal surface is where the reaction happens.",
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          "porosity",
          "tortuosity",
          "active-material",
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        "url": "https://lemonergy.com/learn/glossary/porous-electrode/",
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          "conductive-additive"
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    {
      "id": "term:rate-capability",
      "type": "Term",
      "label": "Rate capability",
      "properties": {
        "id": "rate-capability",
        "name": "Rate capability",
        "section": "topic-ratings",
        "definition": "How much of its capacity a cell can still deliver as the C-rate rises. It is measured by discharging at a series of rates and falls faster for thick, dense electrodes and at low temperature.",
        "related": [
          "c-rate",
          "ideal-duration",
          "polarization",
          "tortuosity",
          "peukert"
        ],
        "url": "https://lemonergy.com/learn/glossary/rate-capability/",
        "mentions": []
      }
    },
    {
      "id": "term:ionic-path",
      "type": "Term",
      "label": "Ionic path",
      "properties": {
        "id": "ionic-path",
        "name": "Ionic path",
        "section": "topic-electrochemistry",
        "definition": "The route lithium ions take: out of one electrode’s particles, through the electrolyte in its pores, across the separator and into the particles of the other electrode. The electrons and ions arrive together, so the slower of the two paths limits the cell.",
        "related": [
          "electronic-path",
          "electrolyte",
          "separator",
          "tortuosity",
          "diffusion",
          "ion"
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        "lesson": "fundamentals/cell-anatomy/#discharge",
        "url": "https://lemonergy.com/learn/glossary/ionic-path/",
        "mentions": [
          "electrode"
        ]
      }
    },
    {
      "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"
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    },
    {
      "id": "term:winding",
      "type": "Term",
      "label": "Winding",
      "properties": {
        "id": "winding",
        "name": "Winding",
        "section": "topic-manufacturing",
        "definition": "Rolling the two electrode strips and two separator strips together around a mandrel into a jelly roll. It is fast and well understood, and it produces the round roll of a cylindrical cell or the flattened roll of many prismatic cells.",
        "related": [
          "jelly-roll",
          "stacking",
          "cylindrical-cell",
          "prismatic-cell"
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        "lesson": "fundamentals/cell-production/#assembly",
        "url": "https://lemonergy.com/learn/glossary/winding/",
        "mentions": [
          "electrode",
          "separator"
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      }
    },
    {
      "id": "lesson:fundamentals/cell-architecture/",
      "type": "Lesson",
      "label": "Lesson 1B · Cell architecture",
      "properties": {
        "url": "https://lemonergy.com/learn/fundamentals/cell-architecture/"
      }
    },
    {
      "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": "<figure class=\"visual-figure\"><figcaption>Effective diffusivity fraction</figcaption><svg class=\"visual-chart\" viewBox=\"0 0 360 330\" role=\"img\" aria-labelledby=\"static-porous-0-title static-porous-0-desc\"><title id=\"static-porous-0-title\">Effective diffusivity fraction</title><desc id=\"static-porous-0-desc\">Porosity ε (fraction) versus D_eff / D (fraction). εᵇ; Straight-pore scaling ε. 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    {
      "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"
      }
    }
  ]
}
