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Lemonergy · Studio block

Single-particle cell

Native spherical solid diffusion and Butler-Volmer kinetics with tabulated electrode OCPs. Isothermal material parameters; no electrolyte transport, aging or conserving adapter.

Implementation ID
battery-single-particle-cell
Reviewed
2026-10-27

Behavior

Solves spherical solid diffusion in separate negative and positive representative particles with conservative radial finite volumes. Opposite Faradaic fluxes transfer lithium between electrodes. Surface stoichiometries drive tabulated OCPs and Butler-Volmer overpotentials; temperature is prescribed.

Interface

Single-particle cell interfaceInputs or arguments on the left, observed outputs on the right. Conserving terminals appear below the component. The tables give units and behavior.Single-particle cellStudio blockcurrenttemperaturevoltagesocNegativesocPositivesurfaceNegativesurfacePositivelithiumconcentrationNegativeconcentrationPositive
Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.
Ports and observed outputs
NameDirectionUnitMeaning
currentinputASigned cell current; scalar.
temperatureinputKKinetics temperature; scalar.
voltageoutputVTerminal voltage; scalar.
socNegativeoutput1 (fraction)Negative-window SOC; scalar.
socPositiveoutput1 (fraction)Positive-window SOC; scalar.
surfaceNegativeoutput1 (fraction)Negative surface stoichiometry; scalar.
surfacePositiveoutput1 (fraction)Positive surface stoichiometry; scalar.
lithiumoutput1Solid lithium inventory (mol); scalar.
concentrationNegativeoutput1Negative shell concentrations (mol/m³); 8 channels at the default configuration.
concentrationPositiveoutput1Positive shell concentrations (mol/m³); 8 channels at the default configuration.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
ParameterUnitDefaultMeaning and limits
Radial shells per particle
shells		18Radial shells per particle. This is an editable model input; the default belongs to the synthetic worked example.
Electrode area (m²)
areaM2		m²0.01Electrode area (m²). This is an editable model input; the default belongs to the synthetic worked example.
Contact resistance (Ω)
resistanceOhm		Ω0.01Contact resistance (Ω). This is an editable model input; the default belongs to the synthetic worked example.
Initial SOC (0–1)
initialSoc		0–10.5Initial SOC (0–1). This is an editable model input; the default belongs to the synthetic worked example.
Negative electrode parameters (see model notes)
negative		See field order[5e-06, 0.0001, 0.5, 30000, 1e-13, 2, 0.1, 0.9]Ordered fields: particle radius (m), electrode thickness (m), solid volume fraction, maximum concentration (mol/m³), diffusion coefficient (m²/s), exchange-current density at half filling (A/m²), empty stoichiometry, full stoichiometry.
Positive electrode parameters (see model notes)
positive		See field order[5e-06, 0.0001, 0.5, 30000, 1e-13, 2, 0.9, 0.1]Ordered fields: particle radius (m), electrode thickness (m), solid volume fraction, maximum concentration (mol/m³), diffusion coefficient (m²/s), exchange-current density at half filling (A/m²), empty stoichiometry, full stoichiometry.
Negative electrode OCP [stoichiometry, V]
negativeOcp		See field order[[0, 0.1], [1, 0.1]]Negative electrode OCP [stoichiometry, V]. Rows are ordered coordinate/value pairs; the first column must be strictly increasing.
Positive electrode OCP [stoichiometry, V]
positiveOcp		See field order[[0, 4.1], [1, 4.1]]Positive electrode OCP [stoichiometry, V]. Rows are ordered coordinate/value pairs; the first column must be strictly increasing.

Equations and rules

  • dc/dt = D/r^2 * d/dr(r^2 * dc/dr)
  • surface molar flux magnitude = I / (F * active particle area)
  • V = Up(surface) - Un(surface) - etaP - etaN - I*Rseries

Worked example

Single-particle cell worked example

Use the defaults below with Signed cell current = 1 A, Kinetics temperature = 298.15 K. At 0 s, Terminal voltage is 3.912048435 V. Additional checks are listed below.

Open Studio example after release →
Numerical checks for the bundled synthetic example
OutputTime (s)Expected valueUnitAbsolute tolerance
Terminal voltage
voltage		03.9120484354726908V1e-08
Negative-window SOC
socNegative		00.51 (fraction)1e-08
Positive-window SOC
socPositive		00.51 (fraction)1e-08
Solid lithium inventory (mol)
lithium		00.01511e-08
Negative-window SOC
socNegative		100.491363108619485231 (fraction)1e-08
Positive-window SOC
socPositive		100.491363108619485231 (fraction)1e-08
Solid lithium inventory (mol)
lithium		100.01511e-10

Explore the recorded outputs

Single-particle cell recorded example

Single-particle cell / Terminal voltage
Single-particle cell / Terminal voltage against timeRecorded synthetic simulation values. Time in seconds; output in V.3.91201403.9120232.53.91203253.9120427.53.91205110VTime (s)
Single-particle cell / Terminal voltage: 3.912048 V at 0 s

103 actual recorded samples. Lines are visual guides between samples. Synthetic example, not measured cell data.

Download the recorded samples (JSON) · Open this Studio example after release

Use in a workflow

Single-particle cell worked example

Native spherical solid diffusion and Butler-Volmer kinetics with tabulated electrode OCPs. Isothermal material parameters; no electrolyte transport, aging or conserving adapter.

  1. Single-particle cell: Solves spherical solid diffusion in separate negative and positive representative particles with conservative radial finite volumes. Opposite Faradaic fluxes transfer lithium between electrodes. Surface stoichiometries drive tabulated OCPs and Butler-Volmer overpotentials; temperature is prescribed.
    • Use the parameter values in the block reference.
    • Implementation tested locally; public release pending.
Open Studio example after release

Connected concepts

Limits and interpretation

  • Fixed solid diffusion and material coefficients; no electrolyte transport, aging, thermal state or conserving boundary adapter. Surface concentrations must stay strictly inside their physical range. The cited paper explains model assumptions and a richer electrolyte extension; this block implements the stated solid-only model.
  • The example verifies numerical behavior for synthetic parameters. Cell characterization and validation for an intended use are separate tasks.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

  1. An asymptotic derivation of a single particle model with electrolyte

    Scott G. Marquis, Valentin Sulzer, Robert Timms, Colin P. Please, S. J. Chapman · Journal of The Electrochemical Society · 2019

    Technical reference · Derivation and validity of reduced lithium-ion particle models, including electrolyte corrections. Background for the assumptions; Lemonergy solid-only SPM does not implement the complete electrolyte extension.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

  • docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)