Calculations
Multiple quick calculations are done within the app to calculate certain parameters. In this section you can find the formulas that belong to these calculations.
- Effective density
The effective density of an electrode coating:
\rho = \sum_i \omega_{i} \rho_i
Here is \omega_{i} the mass fraction of an electrode coating material and \rho_{i} the density of the same coating material.
- Mass loading
The mass loading of an electrode:
\rho A = d \rho(1-\varepsilon)
Here is d the thickness of the electrode coating, \rho is the effective density, and \varepsilon is the porosity.
- Specific capacity
The specific capacity of an active material:
Q_s = c_{max} |x_{max} - x_{min}| \frac{nF}{\rho}
Here is c_{max} the maximum concentration, x_{max} and x_{min} are the maximum and minimum stoichiometry, F is the Faraday constant, \rho the density of the active material, and n is the number of electrons transfered.
- Capacity
The capacity of an electrode:
Q = \omega Q_s \rho V (1-\varepsilon)
Here is \omega the mass fraction, Q_s is the specific capacity, \rho the effective density, V is the volume of the electrode, and \varepsilon is the porosity.
The capacity of the cell is the limiting capacity out of the thwo electrode capacities.
- Cell mass
The cell mass:
m = \sum_i m_{i}
m_i represents here the mass of the several battery components: negative and positive electrode, separator, electrolyte, current collector, and the packing mass.