Exchange-current density functions

ionworkspipeline.direct_entries.arrhenius_butler_volmer_exchange_current_density(electrode: str, direction: str = '', phase: str = '')

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:

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

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, \(T_{ref}\) is the reference temperature, 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.

phasestr, optional

Specifies the phase (“primary” or “secondary”) for composite electrode models. Default is an empty string.