Sodium-ion / Doyle-Fuller-Newman model

The sodium ion model is the same as the lithium ion PXD model, but you have the option to select a slightly adapted Butler-Volmer equation proposed by Chayambuka et al.:

Select this option in your model settings:

model_settings = load_model_settings(;from_file_path = "file_path.json")
model_settings["ButlerVolmer"] = "Chayambuka"

Butler-Volmer equation

$$j=j_0[\frac{c_s^s}{{\overline{c}}_s}\exp \left(\frac{\alpha F}{RT}\mu \right)-\frac{c_s^{max}-c_s^s}{c_s^{max}-\overline{c_s}}\frac{c_e}{\overline{c_e}}\exp (-\frac{(1-\alpha )F}{RT}\mu )].$$

Here is ${\sigma }_{\text{eff}}$ the charge transfer coefficient, $\mu$ is the charge transfer overpotential, $c_s^s$ is the electrode surface concentration of sodium, $\overline{c_s}$ is the average particle concentration, $c_s^{max}$ the solid saturation concentration, $c_e$, the electrolyte concentration, and $\overline{c_e}$ the average sodium concentration in the electrolyte. The exchange current density can be expressed as:

$$j_0=Fk(c_s^{max}-\overline{c_s}{)}^{{\alpha }_a}(\overline{c_e}{)}^{{\alpha }_a}(\overline{c_s}{)}^{{\alpha }_c},$$

where $k$ is the reaction rate constant.