Exchange-current density functions

ionworkspipeline.direct_entries.arrhenius_butler_volmer_exchange_current_density(electrode, direction='')

Returns a DirectEntry object with the standard Butler-Volmer exchange-current functions for the negative or positive electrode, with arrhenius temperature dependence.

These functions are of the form:

\[j_0 = j_0^{ref} (c_e / c_{e,0})^{0.5} (c_{s,surf} / c_{s,max})^{0.5} (1 - c_{s,surf} / c_{s,max})^{0.5} \exp(E_r / R (1 / 298.15 - 1 / T))\]

where \(j_0^{ref}\) is the reference exchange-current density, \(c_e\) is the electrolyte concentration, \(c_{e,0}\) is the initial electrolyte concentration, \(c_{s,surf}\) is the surface concentration of the solid phase, \(c_{s,max}\) is the maximum solid concentration, \(E\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature.

This leaves the following parameters to be defined (e.g. by fitting to data):

• Negative/Positive electrode reference exchange-current density [A.m-2]

  ($j_0^{ref}$)

• Negative/Positive electrode reaction activation energy [J.mol-1] ($E_r$)

Parameters

electrodestr

The electrode to return the exchange-current function for. Must be “negative” or “positive”.

directionstr, optional

The direction of the exchange-current density. Can be “lithiation” or “delithiation” or an empty string.