Doyle-Fuller-Newman (DFN) battery model

The DFN model, also called P2D or the Newman model, is the canonical physics-based model for a lithium-ion cell. Full porous electrode theory. Spatially resolved transport. The benchmark against which every reduced-order model is compared.

DFN is the right model when your engineering question depends on where something happens inside the electrode: lithium plating near the separator, gradients in graded architectures, mechanism-level degradation. Reduced-order SPM and SPMe models are faster but cannot resolve those gradients.

Book a demo

Doyle-Fuller-Newman (DFN) battery model schematic showing lithium transport through the electrolyte and intercalation into solid particles across the negative electrode, separator, and positive electrode

DFN model structure: porous electrodes, electrolyte transport, particle diffusion

What DFN captures

DFN implements full porous electrode theory. Both electrodes are treated as porous media with spatially resolved transport in the electrolyte and solid phases. Intercalation kinetics, charge conservation, and species transport are coupled across a 1D domain spanning the anode, separator, and cathode. Inside each electrode, a "pseudo" radial dimension inside the particles tracks solid-state lithium diffusion (this is why the model is also called P2D).

The model is invoked in PyBaMM as pybamm.lithium_ion.DFN(). It serves two roles in practice: it is the working model for studies that need spatial physics, and it is the reference model that reduced-order SPM and SPMe are validated against.

Inside the model

Porous electrodes

Spatially resolved transport

Both electrodes are treated as porous media. Lithium concentration in the electrolyte and in the solid phase varies through the thickness of the electrode stack. The model resolves what happens at the separator versus at the current collector.

Electrolyte transport

Concentration and potential gradients

Concentrated solution theory tracks lithium-ion concentration and electrolyte potential across the anode, separator, and cathode. Transport limitations and ohmic drops are observable, not lumped.

Solid diffusion

Per-electrode particle physics

Each electrode has its own particle population, intercalation kinetics, and OCV curve. Anode and cathode contributions to the cell voltage are separable, and electrode-specific overpotentials are inspectable.

Coupled physics

Reference for reduced-order models

DFN is the benchmark against which SPM and SPMe are compared. Every PyBaMM degradation submodel (SEI, plating, LAM, particle cracking) attaches to the DFN framework.

Spatial resolution: the differentiator

The defining advantage of DFN over reduced-order models is spatial resolution within the electrode. Anode potential is not uniform across the electrode thickness. Near the separator, where lithium flux peaks during charging, the anode potential drops lower than near the current collector. Plating risk is highest in that region, and DFN captures the gradient that determines whether plating occurs and where. SPM and SPMe average over the electrode thickness and cannot see this.

The same principle applies to non-uniform porosity in graded electrodes, to reaction-rate distributions that shift with C-rate and temperature, and to electrolyte depletion profiles that vary spatially through the stack. If your question involves where something happens within the electrode, not just whether it happens, DFN is required.

DFN at a glance

Dimension	DFN
Physics captured	Full porous electrode theory + electrolyte transport
Parameterization burden	High (35+ parameters, teardown + half-cell typical)
Compute cost	High (coupled PDEs, expensive for sweeps)
Accuracy	Benchmark for lithium-ion cell models
Degradation capability	Full mechanism-level (SEI, plating, cracking, LAM)
Best fit	Plating studies, design optimization, fast charge, low temperature

For a side-by-side comparison with ECM, SPM, and SPMe, see the electrochemical model types resource.

When DFN is the right model

DFN earns its parameterization and compute cost when the engineering question depends on spatial physics. Three patterns recur.

Fast-charge envelope

Anode potential drops below 0 V vs. Li/Li⁺ near the separator first. DFN resolves that gradient, which is what determines plating onset and where it occurs.

Electrode design

Coating thickness, porosity profiles, particle size distributions, and graded architectures all change cell behavior through spatial mechanisms that SPM and SPMe average away.

Mechanism-level degradation

SEI growth on freshly cracked surfaces, position-dependent plating, electrolyte depletion profiles. Each of these is spatially distributed inside the electrode.

Where DFN is overkill: low-rate calendar studies, first-pass design sweeps over hundreds of points, real-time onboard estimation in a BMS. Those are SPM, SPMe, or ECM territory. The right rule of thumb: start with the lowest-fidelity model that answers the question, and step up only when the physics demand it.

Beyond standard 1D DFN

Standard DFN assumes a single active material per electrode and a monotonic OCV curve. Several important chemistries and cell geometries violate those assumptions.

Composite electrodes. Graphite-silicon blends are the most common case. PyBaMM's BasicDFNComposite models each active material phase with its own particle diffusion and OCV curve, capturing the differential lithiation between graphite and silicon domains.

Hysteresis. LFP and silicon chemistries exhibit OCV hysteresis: the voltage on charge differs from the voltage on discharge at the same SoC. PyBaMM includes hysteresis state models that track the charge/discharge branch and matter for SoC estimation accuracy and for path-dependent degradation prediction.

MSMR thermodynamics. The Multi-Species Multi-Reaction framework (Yang et al. 2017) models multiple intercalation reactions within a single electrode particle, capturing graphite staging plateaus and NMC phase transitions with higher thermodynamic accuracy than a fitted polynomial OCV.

3D extension. Large-format pouch and prismatic cells have in-plane gradients that 1D DFN cannot see. Tab placement affects internal resistance distribution; temperature hotspots localize near tabs. Pseudo-3D and full 3D electrochemical models resolve these gradients without rewriting the parameter set.

Parameterization is the bottleneck

DFN parameterization is the heaviest in the model hierarchy. Half-cell OCV curves for both electrodes. A full-cell OCV characterization. Geometric parameters from teardown: electrode dimensions, particle sizes, porosities, active material volume fractions. Rate capability tests to fit transport and kinetic properties as functions of temperature and SoC. Chen et al. (2020) demonstrated 35+ parameters for a single LG M50 21700 cell.

A solver runs in seconds. Assembling a defensible parameter set often takes weeks. Identifiability is harder than fit quality: a parameterization that pushes correlated parameters in opposite directions can fit one curve perfectly and fail on the next one. Our parameter estimation guide covers the DFN data requirements step by step.

This is the Train stage in Ionworks Studio. A DFN parameter set fit here drives every downstream study, including 3D electrochemical simulations of the same cell, without re-fitting.

How Ionworks fits in

How Ionworks supports DFN

PyBaMM as the DFN solver

Ionworks runs DFN through PyBaMM (`pybamm.lithium_ion.DFN()`), the open-source framework maintained by the Ionworks team. The same parameter set drives DFN, SPMe, and SPM, so the model choice is a setting in the workflow, not a re-parameterization.

Parameterization with provenance

A 35+ parameter set is too large to manage by spreadsheet. Each parameter is recorded with its source: which experiment it was fit to, which literature reference it came from, which cell it belongs to. Studies six months later are reproducible because the provenance travels with the parameter set.

Identifiability and uncertainty

Global optimization with multistart, Bayesian priors, and uncertainty quantification flag parameters that the data leaves under-constrained. A defensible parameter set is more useful than a precise-looking one.

BPX import and export

Ionworks supports BPX, the community standard for physics-based battery parameter sets. Vendor-supplied BPX files load directly. Internal parameter sets export to BPX for sharing with partners and suppliers without translation.

1D to 3D without rewriting

A DFN parameter set fit on cycling data carries forward into 3D electrochemical simulations of the same cell. Tab placement, hotspots, and in-plane gradients are studied without maintaining a separate parameter set in a different tool.

Ionworks Studio Train stage: DFN parameterization workflow with provenance, identifiability checks, and BPX export

DFN parameterization in Ionworks Studio

Frequently asked questions

The Doyle-Fuller-Newman model, also called P2D or the Newman model, is the canonical physics-based model for a lithium-ion cell. It implements full porous electrode theory: both electrodes are treated as porous media with spatially resolved transport in the electrolyte and solid phases, coupled to Butler-Volmer kinetics at the particle surface. Charge conservation, species transport, and intercalation kinetics are solved together across a 1D domain spanning the anode, separator, and cathode. DFN is the reference model that reduced-order models like SPM and SPMe are derived from and compared against.

They are the same model. DFN refers to the original Doyle, Fuller, and Newman formulation; P2D (pseudo-2D) refers to the same equations described by their dimensionality: one spatial dimension across the cell sandwich, plus a "pseudo" radial dimension inside each particle. PyBaMM exposes the model as pybamm.lithium_ion.DFN(). Some papers use one term, some use the other, and they are interchangeable in the literature.

Use DFN when your engineering question depends on where something happens within the electrode, not just whether it happens. Lithium plating risk is the standard example: anode potential drops lowest near the separator, which is where plating starts, and SPMe averages over the electrode thickness so it cannot resolve that gradient. Other DFN-required questions include electrode design (coating thickness, porosity, particle size optimization), mechanism-level degradation studies that need spatially resolved SEI or cracking, and graded electrode architectures. For fast-charge envelope studies that do not yet need plating prediction, calendar aging, and cycle life screening, SPMe is usually sufficient and much cheaper.

DFN parameterization is the heaviest in the electrochemical model hierarchy. A typical parameter set includes half-cell OCV curves for both electrodes, a full-cell OCV characterization, geometric parameters from teardown (electrode dimensions, particle sizes, porosities, active material volume fractions), and rate capability tests to fit transport and kinetic properties as functions of temperature and SoC. Chen et al. (2020) demonstrated 35+ parameters for a single LG M50 21700 cell. The solver runs in seconds; assembling a defensible parameter set often takes weeks. Ionworks Studio handles the fitting workflow in Train and supports BPX parameter exchange.

DFN solves coupled PDEs for solid diffusion in both electrodes and electrolyte transport across the full electrode thickness. SPM solves one PDE for solid diffusion with algebraic equations elsewhere. In practice DFN is roughly 10 to 100 times slower than SPM, and roughly 5 to 50 times slower than SPMe, depending on the simulation. Individual DFN solves are tractable. Large parameter sweeps and outer-loop optimization studies are where the cost dominates, and many teams use SPMe for screening and DFN only for the targeted studies that need spatial physics.

Yes, and this is one of the main reasons to use DFN. Every PyBaMM degradation submodel (SEI growth, lithium plating, loss of active material, particle cracking, electrolyte depletion) attaches to the DFN framework. Mechanism-level coupling, where particle cracking exposes fresh surface that accelerates SEI growth, runs on DFN within a single coupled simulation. Reduced-order models can support some of these mechanisms approximately, but the full coupling and spatial resolution come from DFN.

Yes. Ionworks is built on PyBaMM and treats models as first-class objects. Teams can bring custom PyBaMM models, modified DFN variants, or new submodels, and run them through the same parameterization, simulation, and optimization workflow as the built-in DFN. Composite electrode models (graphite-silicon blends with BasicDFNComposite), MSMR thermodynamics, and OCV hysteresis variants are all supported.

See DFN running on your cell, with full parameter provenance

Bring a dataset and a parameter set, or start from one of ours. We will show what DFN catches that SPMe averages away, and where the cost pays for itself.

Book a demo