Source code for mtnlion.models.sei

"""
Isothermal model extended with SEI layer growth
"""
import dolfin as fem

from mtnlion.formula import Formula, Variable
from mtnlion.formulas.dfn import CapacityLoss, FilmResistance, FilmThickness
from mtnlion.models.isothermal import Isothermal

# pylint: disable=invalid-name


class SEI(Isothermal):
    """
    The SEI model is an extension to the isothermal model that attempts to quantify solid-electrolyte interphase
    formation and growth on the negative-electrode solid particles during chargning.
    """

    def __init__(self, Ns):
        super(SEI, self).__init__(Ns)

        self.variables += [Variable("j_s", ["anode"]), Variable("delta_film", ["anode"]), Variable("Q", ["anode"])]

        self.formulas += [
            self.SideReactionFlux(),
            self.SideReactionOverpotential(),
            FilmThickness(),
            FilmResistance(),
            CapacityLoss(),
            self.LocalMolecularFlux(),
        ]

    class Overpotential(Formula):
        """
        Voltage difference between a reduction potential and the potential of the redox event.
        """

        def __init__(self):
            super(SEI.Overpotential, self).__init__(name="eta", domains=["anode", "cathode"])
            self.Variables = self.typedef("Variables", "phi_s, phi_e, j")
            self.Parameters = self.typedef("Parameters", "F, Uocp, Rfilm, j_total")

        def form(self, arguments, domain):  # pylint: disable=R1710
            phis, phie, j = arguments.variables
            (F, Uocp, Rfilm, j_total) = arguments.parameters

            if domain == "anode":
                return phis - phie - Uocp - F * Rfilm * j_total

            if domain == "cathode":
                Rfilm = 0
                return phis - phie - Uocp - F * Rfilm * j

    class LocalMolecularFlux(Formula):
        """
        The total flux of the system including intercalation flux and side reaction flux.
        """

        def __init__(self):
            super(SEI.LocalMolecularFlux, self).__init__(name="j_total", domains=["anode"])
            self.Variables = self.typedef("Variables", "j, j_s")

        def form(self, arguments, domain):
            j, js = arguments.variables

            return j + js

    class SideReactionFlux(Formula):
        """
        Describes how the electrical current on an electrode depends on the electrode potential due to the side
        reaction.
        """

        def __init__(self):
            super(SEI.SideReactionFlux, self).__init__(domains=["anode"])
            self.Variables = self.typedef("Variables", "j_s")
            self.Parameters = self.typedef("Parameters", "io_sei, alpha, F, R, T, eta_s")

        def form(self, arguments, domain):
            """Flux through the boundary of the solid."""
            (js,) = arguments.variables
            io_sei, alpha, F, R, T, eta_s = arguments.parameters

            return (js + io_sei / F * fem.exp(-alpha * F * eta_s / (R * T))) * js.test()

    class SideReactionOverpotential(Formula):
        """
        Voltage difference between a reduction potential and the potential of the redox event in the side reaction.
        """

        def __init__(self):
            super(SEI.SideReactionOverpotential, self).__init__(name="eta_s", domains=["anode"])
            self.Variables = self.typedef("Variables", "phi_s, phi_e")
            self.Parameters = self.typedef("Parameters", "Uref_s, F, Rfilm, j_total")

        def form(self, arguments, domain):
            phis, phie = arguments.variables
            Uref_sei, F, Rfilm, j_total = arguments.parameters

            return phis - phie - Uref_sei - F * Rfilm * j_total