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.