Source code for pybamm.models.submodels.electrode.ohm.li_metal
#
# Subodels for a lithium metal electrode
#
import pybamm
from .base_ohm import BaseModel
class LithiumMetalBaseModel(BaseModel):
def __init__(self, param, domain, options=None):
super().__init__(param, domain, options=options)
def _get_li_metal_interface_variables(self, delta_phi_s, phi_s, phi_e):
domain, Domain = self.domain_Domain
variables = {
f"{Domain} electrode potential drop [V]": delta_phi_s,
f"X-averaged {domain} electrode ohmic losses [V]": delta_phi_s / 2,
"Lithium metal interface electrode potential [V]": phi_s,
"Lithium metal interface electrolyte potential [V]": phi_e,
}
return variables
class LithiumMetalSurfaceForm(LithiumMetalBaseModel):
"""Model for potential drop across a lithium metal electrode, with a
differential or algebraic equation for the surface potential difference
Parameters
----------
param : parameter class
The parameters to use for this submodel
domain : str
The domain of the submodel, can be "negative" or "positive"
options : dict, optional
A dictionary of options to be passed to the model.
"""
def get_fundamental_variables(self):
delta_phi = pybamm.Variable(
"Lithium metal interface surface potential difference [V]",
domain="current collector",
)
variables = {
"Lithium metal interface surface potential difference [V]": delta_phi,
}
return variables
def get_coupled_variables(self, variables):
Domain = self.domain.capitalize()
domain_param = self.domain_param
i_boundary_cc = variables["Current collector current density [A.m-2]"]
T = variables[f"{Domain} current collector temperature [K]"]
L = domain_param.L
delta_phi_s = i_boundary_cc * L / domain_param.sigma(T)
phi_s_cc = variables[f"{Domain} current collector potential [V]"]
delta_phi = variables[
"Lithium metal interface surface potential difference [V]"
]
# Potentials at the anode/separator interface
phi_s = phi_s_cc - delta_phi_s
phi_e = phi_s - delta_phi
variables.update(
self._get_li_metal_interface_variables(delta_phi_s, phi_s, phi_e)
)
return variables
def set_initial_conditions(self, variables):
delta_phi = variables[
"Lithium metal interface surface potential difference [V]"
]
delta_phi_init = self.domain_param.prim.U_init
self.initial_conditions = {delta_phi: delta_phi_init}
def set_rhs(self, variables):
Domain = self.domain.capitalize()
if self.options["surface form"] == "differential":
j_pl = variables["Lithium metal plating current density [A.m-2]"]
j_sei = variables[
f"{Domain} electrode SEI interfacial current density [A.m-2]"
]
sum_j = j_pl + j_sei
i_cc = variables["Current collector current density [A.m-2]"]
delta_phi = variables[
"Lithium metal interface surface potential difference [V]"
]
# temperature at the interface of the negative electrode with the separator
T = pybamm.boundary_value(
variables["Negative electrode temperature [K]"], "right"
)
C_dl = self.domain_param.C_dl(T)
self.rhs[delta_phi] = 1 / C_dl * (i_cc - sum_j)
def set_algebraic(self, variables):
Domain = self.domain.capitalize()
if self.options["surface form"] != "differential": # also catches "false"
j_pl = variables["Lithium metal plating current density [A.m-2]"]
j_sei = variables[
f"{Domain} electrode SEI interfacial current density [A.m-2]"
]
sum_j = j_pl + j_sei
i_cc = variables["Current collector current density [A.m-2]"]
delta_phi = variables[
"Lithium metal interface surface potential difference [V]"
]
self.algebraic[delta_phi] = (i_cc - sum_j) / self.param.I_typ
