メインコンテンツへスキップ
Geometric and capacity parameters define the physical structure of a battery cell and its energy storage capability. These calculations are foundational for building accurate battery models.

​
The Capacity Equation

Electrode capacity is determined by geometry and material properties: Q=cmax⁡⋅εAM⋅L⋅A⋅nelec⋅(θmax⁡−θmin⁡)⋅F3600Q = c_{\max} \cdot \varepsilon_{\text{AM}} \cdot L \cdot A \cdot n_{\text{elec}} \cdot (\theta_{\max} - \theta_{\min}) \cdot \frac{F}{3600} where:
  • QQ is the electrode capacity [A·h]
  • cmax⁡c_{\max} is the maximum lithium concentration [mol/m³]
  • εAM\varepsilon_{\text{AM}} is the active material volume fraction
  • LL is the electrode thickness [m]
  • AA is the electrode area [m²]
  • nelecn_{\text{elec}} is the number of electrodes connected in parallel (defaults to 1)
  • θmax⁡−θmin⁡\theta_{\max} - \theta_{\min} is the usable stoichiometry range
  • F=96485F = 96485 C/mol is Faraday’s constant
This equation relates six parameters (seven when nelecn_{\text{elec}} is specified)—if you know all but one, you can solve for it. For example, when capacity is known, the ElectrodeCapacity calculation can solve for maximum concentration; supply any five of the six parameters and it returns the missing one.
パイプラインでこれらの計算を構成する方法については、Pipelines → Calculations → Geometry & Capacity を参照してください。

​
Cell Geometry

​
Geometry Hierarchy

Battery cells are organized hierarchically:

​
Key Parameters

For pouch and prismatic cells, electrode area is the planar area times the number of layers. For cylindrical cells, it’s the unrolled electrode area.

​
Cyclable Lithium

Cyclable lithium is the total lithium that shuttles between electrodes during cycling. It sets the upper limit on cell capacity. QLi=θn⋅Qn+θp⋅QpQ_{\text{Li}} = \theta_n \cdot Q_n + \theta_p \cdot Q_p where stoichiometries θn,θp\theta_n, \theta_p are evaluated at a reference state (typically 100% SOC).

​
Why It Matters

  • Cell capacity: Cannot exceed cyclable lithium, regardless of electrode capacities
  • Degradation tracking: Loss of cyclable lithium indicates SEI growth, plating, or particle cracking
  • Electrode balancing: Determines which electrode limits cell capacity

​
N/P Ratio and Electrode Balancing

The negative-to-positive capacity ratio (N/P ratio) affects how electrodes are utilized: N/P ratio=QnQp\text{N/P ratio} = \frac{Q_n}{Q_p}
Cells are typically designed with N/P > 1 to prevent lithium plating at the negative electrode during charge.

​
Mass Calculations

Mass is needed for gravimetric energy density and thermal modeling.

​
Component Mass

Each component’s mass is calculated from: m=ρ⋅A⋅L⋅(1−ε)m = \rho \cdot A \cdot L \cdot (1 - \varepsilon) where ρ\rho is density, AA is area, LL is thickness, and ε\varepsilon is porosity.

​
Energy Density

Gravimetric and volumetric energy densities are key cell-level metrics: Egrav=Q⋅Vavgmcell,Evol=Q⋅VavgVcellE_{\text{grav}} = \frac{Q \cdot V_{\text{avg}}}{m_{\text{cell}}}, \quad E_{\text{vol}} = \frac{Q \cdot V_{\text{avg}}}{V_{\text{cell}}}

​
Microstructure

Microstructure parameters describe the porous electrode architecture:

​
Porosity

The void fraction of the electrode: ε=1−εAM−εbinder−εcarbon\varepsilon = 1 - \varepsilon_{\text{AM}} - \varepsilon_{\text{binder}} - \varepsilon_{\text{carbon}} Higher porosity improves electrolyte transport but reduces energy density.

​
Tortuosity

Describes how much longer the effective transport path is compared to the straight-line distance: Deff=D⋅ετD_{\text{eff}} = \frac{D \cdot \varepsilon}{\tau} Common correlations relate tortuosity to porosity:
  • Bruggeman: τ=ε−0.5\tau = \varepsilon^{-0.5}
  • Measured: From electrochemical impedance or other techniques

​
Active Material Volume Fraction

The fraction of electrode volume occupied by active material: εAM=VAMVelectrode\varepsilon_{\text{AM}} = \frac{V_{\text{AM}}}{V_{\text{electrode}}} This is a key fitting parameter affecting both capacity and transport.

​
Practical Workflow

1

Define Geometry

Set electrode area, thicknesses, and number of layers
2

Specify Microstructure

Set active material volume fractions and calculate porosity
3

Calculate Capacities

Use ElectrodeCapacity for each electrode
4

Determine Cyclable Lithium

Use CyclableLithium to find the limiting capacity
5

Calculate Mass and Energy Density

Use CellMass to roll the component contributions up to a cell-level mass

​
Common Calculations