This node is available as a subnode to the Porous Electrode and Additional Porous Electrode Material nodes in The Lithium-Ion Battery Interface and The Battery with Binary Electrolyte Interface interfaces. The node is only visible if Intercalating Particles has been selected on the parent node.

The Initial species concentration cs,init (SI unit: mol/m3) is used by the solver and can be used to specify the initial state-of-charge of the electrode.

The Maximum species concentration cs,max (SI unit: mol/m3) defines the maximum possible concentration of the intercalated concentration. The value is used by Porous Electrode Reaction when the Kinetic expression type has been set to Lithium Insertion.

The Species concentration transport model specifies the diffusion model for the intercalating species in the electrode particles.

Fick’s law and Baker-Verbrugge both add an extra dimension, defined on the porous electrode domain, within which a diffusion equation is applied in order to solve for the concentration distribution along the depth within a single particle of the electrode. The transport in the extra dimension is defined by the Intercalation diffusivity Ds (SI unit: m2/s).

Fick’s law defines the molecular flux of the intercalated species as the product of the diffusion coefficient and the concentration gradient. The Baker-Verbrugge models adds a correction to the diffusion coefficient based on the Equilibrium potential, Eeq, of the intercalation reaction. This potential is defined in the Equilibrium Potential section below. Generally, the Baker-Verbrugge model is better at capturing state-of-charge dependent transport rates and staging phenomena, whereas Fick’s law may be numerically more stable. Note that the parameter values of the diffusivity from the material library generally have been estimated assuming Fick’s law and may have to be reduced when switching to Baker-Verbrugge.

Use No spatial gradients to assume a constant concentration along the depth of the particle. No spatial gradients significantly reduces the computational load of the model.

The geometry in the extra dimension is one-dimensional and is defined by the Particle type (Spheres (the default), Cylinders, or Flakes) together with the Particle mean center-surface distance rp.

Use the Minimum and the Maximum electrode state-of-charge, SOCmin (dimensionless) and SOCmax (dimensionless) to specify a nominal state-of-charge window for the electrode. These values are used together with the Initial Cell Charge Distribution node to define an initial cell state of charge.

This section is not available if No spatial gradients is selected under Particle Transport Settings.

Use these settings to control the Distribution of the mesh and the Element order of the extra particle dimension.

The predefined distributions Square or Cubic root sequence create mesh distributions with a denser mesh toward the particle surface.

The Use fast assembly in particle dimension option enables an alternative method for assembling of the diffusion equation in the particle dimension that may decrease computation time when the number of mesh elements in the battery cell dimension is of the same order of magnitude as the number of elements in the particle dimension (this is typically the case for 1D problems). When the fast assembly option is enabled, it is not possible to postprocess the solid particle concentration along the particle dimension, and the diffusion coefficient in the particle cannot vary along the particle depth. The same equations are solved for regardless of assembly method.

The fast assembly option is not available if Baker-Verbrugge species concentration transport model is enabled.

This section is not available if No spatial gradients is selected under Particle Transport Settings, or if Use fast assembly in particle dimension is enabled under Particle Discretization.

Include heat of mixing defines a heat source defined as the gradient of the molar enthalpy times the molar flux of the intercalating species, integrates it over the particle, and adds it to the total heat source variable in the domain. The molar enthalpy is based on the Equilibrium potential of the insertion reaction, defined below.

The heat source is typically used when coupling the battery interface to a heat transfer interface using the Electrochemical Heating node.

This section defines the Equilibrium potential of the intercalation reaction, Eeq (SI unit: V), used by the Particle Transport Properties and Heat of Mixing sections, when applicable.

This section is not available if No spatial gradients or the particle type Flakes is selected under Particle Transport Settings, or if Use fast assembly in particle dimension is enabled under Particle Discretization.

When modeling diffusion in the particle you may enable the Calculate stress and strain check box to compute a number stress and strain related variables in the particle. The variables are based on the Young’s modulus, the Poisson’s ration and the relative volume change of the particle. The relative volume change is typically dependent on the concentration in the particle.

See also Stress and strain in intercalating particles in the theory chapter below.