{ "node": { "id": "term:concentration-gradient", "type": "Term", "label": "Concentration gradient", "properties": { "id": "concentration-gradient", "name": "Concentration gradient", "section": "topic-transport", "definition": "The rate at which concentration changes with distance, dc/dx, in mol/m⁴. It is the driving force in Fick’s law; current creates one across the electrolyte and inside each particle, and it relaxes away when current stops.", "unit": "mol/m⁴", "related": [ "ficks-first-law", "concentration-polarization", "relaxation", "diffusion" ], "lesson": "transport/ficks-first-law/#sign", "url": "https://lemonergy.com/learn/glossary/concentration-gradient/", "mentions": [ "electrolyte" ] } }, "edges": [ { "id": "edge:28", "source": "term:concentration-gradient", "target": "workflow:fick-flux", "type": "usedIn", "properties": { "sourceFile": "wiki-blocks.json" } }, { "id": "edge:2065", "source": "term:concentration-gradient", "target": "topic:topic-transport", "type": "belongsTo", "properties": { "sourceFile": "terms.json" } }, { "id": "edge:2066", "source": "term:concentration-gradient", "target": "term:ficks-first-law", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2067", "source": "term:concentration-gradient", "target": "term:concentration-polarization", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2068", "source": "term:concentration-gradient", "target": "term:relaxation", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:2069", "source": "term:concentration-gradient", "target": "term:diffusion", "type": "relatedTo", "properties": { "sourceFile": "terms.json", "meaning": "Related context; not a causal claim" } }, { "id": "edge:mentions/concentration-gradient/electrolyte", "source": "term:concentration-gradient", "target": "term:electrolyte", "type": "mentions", "properties": { "sourceFile": "terms.json", "method": "build_glossary.mention_index + mentions", "field": "definition", "meaning": "Text mention; not a causal claim" } }, { "id": "edge:2071", "source": "term:concentration-gradient", "target": "lesson:transport/ficks-first-law/", "type": "explainedIn", "properties": { "sourceFile": "terms.json", "url": "https://lemonergy.com/learn/transport/ficks-first-law/#sign" } }, { "id": "edge:2072", "source": "term:concentration-gradient", "target": "visual:diffusion", "type": "illustratedBy", "properties": { "sourceFile": "visual-pages.json" } }, { "id": "edge:2073", "source": "term:concentration-gradient", "target": "reference:iupac-green", "type": "cites", "properties": { "sourceFile": "wiki-references.json", "scope": "direct technical reference" } } ], "neighbors": [ { "id": "workflow:fick-flux", "type": "Workflow", "label": "Calculate diffusion flux", "properties": { "id": "fick-flux", "title": "Calculate diffusion flux", "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": "For D = 1 × 10⁻¹⁰ m²/s and dc/dx = 2 × 10⁶ mol/m⁴, J = −2 × 10⁻⁴ mol/(m²·s).", "observe": "Compare the result with the equation and units.", "limits": "This does not solve second-law time evolution or specify boundary conditions.", "url": "https://lemonergy.com/learn/transport/ficks-first-law/", "label": "Open the worked lesson", "evidence": [ "src/battery_core/diffusion.py" ] } }, { "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:ficks-first-law", "type": "Term", "label": "Fick’s first law", "properties": { "id": "ficks-first-law", "name": "Fick’s first law", "section": "topic-transport", "definition": "J = −D dc/dx: diffusive flux is proportional to the concentration gradient and points down it. It is a constitutive law, valid at one instant; Fick’s second law follows from it when mass is conserved.", "formula": "J = −D · dc/dx", "unit": "mol/(m²·s)", "related": [ "diffusion-coefficient", "concentration-gradient", "ficks-second-law", "diffusion" ], "lesson": "transport/ficks-first-law/", "example": { "title": "Read the direction of a flux", "text": "With D = 1×10⁻¹⁰ m²/s and dc/dx = 1×10⁶ mol/m⁴, J = −1×10⁻⁴ mol/(m²·s). The negative sign means diffusion points toward decreasing concentration." }, "url": "https://lemonergy.com/learn/glossary/ficks-first-law/", "mentions": [] } }, { "id": "term:concentration-polarization", "type": "Term", "label": "Concentration polarization", "properties": { "id": "concentration-polarization", "name": "Concentration polarization", "section": "topic-electrochemistry", "definition": "Voltage loss that arises when reactant is consumed faster than diffusion can replace it, so the concentration at the surface differs from the bulk. It dominates at high current and low temperature and recovers slowly when current stops.", "related": [ "polarization", "diffusion", "overpotential", "relaxation", "concentration-gradient" ], "url": "https://lemonergy.com/learn/glossary/concentration-polarization/", "mentions": [] } }, { "id": "term:relaxation", "type": "Term", "label": "Relaxation", "properties": { "id": "relaxation", "name": "Relaxation", "aka": [ "rest" ], "section": "topic-charging", "definition": "The slow recovery of a cell’s voltage towards open-circuit voltage after current stops, as concentration gradients inside the electrodes level out. It takes minutes to hours, which is why OCV measurements need a rest period.", "related": [ "open-circuit-voltage", "polarization", "diffusion", "hppc", "voltage-relaxation-analysis" ], "url": "https://lemonergy.com/learn/glossary/relaxation/", "mentions": [] } }, { "id": "term:diffusion", "type": "Term", "label": "Diffusion", "properties": { "id": "diffusion", "name": "Diffusion", "section": "topic-transport", "definition": "The net movement of a species from where it is concentrated to where it is scarce, driven by random thermal motion. In a cell lithium diffuses through the electrolyte in the pores and, far more slowly, through the solid particles themselves.", "related": [ "ficks-first-law", "diffusion-coefficient", "solid-state-diffusion", "concentration-gradient", "migration" ], "lesson": "transport/ficks-first-law/#in-a-cell", "url": "https://lemonergy.com/learn/glossary/diffusion/", "mentions": [ "electrolyte" ] } }, { "id": "term:electrolyte", "type": "Term", "label": "Electrolyte", "properties": { "id": "electrolyte", "name": "Electrolyte", "section": "topic-electrolytes", "definition": "The ion-conducting medium between the electrodes. In a liquid-electrolyte cell it fills the pores of both electrodes and the separator, so it is not a separate structural layer.", "related": [ "lithium-salt", "carbonate-solvent", "electrolyte-additive", "ionic-conductivity", "solid-electrolyte", "ionic-liquid-electrolyte" ], "lesson": "fundamentals/cell-architecture/#electrolyte", "example": { "title": "Ions and electrons", "text": "Electrolyte carries ions between electrodes; the external circuit carries electrons. The two paths serve different roles." }, "url": "https://lemonergy.com/learn/glossary/electrolyte/", "mentions": [ "separator" ] } }, { "id": "lesson:transport/ficks-first-law/", "type": "Lesson", "label": "Fick’s first law", "properties": { "url": "https://lemonergy.com/learn/transport/ficks-first-law/" } }, { "id": "visual:diffusion", "type": "Visual", "label": "Flux follows the concentration slope", "properties": { "title": "Flux follows the concentration slope", "summary": "The minus sign in Fick’s law sends material down its concentration gradient.", "readout": "Flux J = 500 μmol/(m²·s), toward increasing position.", "formula": "J = −D dc/dx", "note": "The profile is imposed and static. Time evolution requires Fick’s second law and boundary conditions.", "software": { "status": "implemented", "label": "Implemented in battery-core", "body": "ficks_first_law_flux evaluates J = −D dc/dx. It does not solve a diffusion PDE, estimate the gradient or apply boundary conditions.", "href": "../transport/ficks-first-law/" }, "html": "
Imposed concentration profile
Imposed concentration profilePosition (μm) versus Concentration (mol/m³). Concentration. Interpretation follows the graphs.00500251,000501,500752,000100Position (μm)Concentration (mol/m³)
Concentration
" } }, { "id": "reference:iupac-green", "type": "Reference", "label": "Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing", "properties": { "title": "Quantities, Units and Symbols in Physical Chemistry, 3rd edition, 2nd printing", "publisher": "IUPAC", "url": "https://media.iupac.org/publications/books/gbook/IUPAC-GB3-2ndPrinting-Online-22apr2011.pdf", "type": "Technical reference", "scope": "Physical-chemistry notation, thermodynamics, electrochemistry and transport quantities.", "year": 2011, "accessed": "2026-10-27" } } ] }