Tunnelling limited has been added for SEI growth

pybamm-team · Sep 23, 2024 · c08bdb6 · c08bdb6
1 parent 94311f6
commit c08bdb6
Show file tree

Hide file tree

Showing 3 changed files with 14 additions and 0 deletions.
diff --git a/src/pybamm/models/full_battery_models/base_battery_model.py b/src/pybamm/models/full_battery_models/base_battery_model.py
@@ -303,6 +303,7 @@ def __init__(self, extra_options):
                 "ec reaction limited",
                 "ec reaction limited (asymmetric)",
                 "Kolzenberg2020",
+                "tunnelling limited",
             ],
             "SEI film resistance": ["none", "distributed", "average"],
             "SEI on cracks": ["false", "true"],

diff --git a/src/pybamm/models/submodels/interface/sei/sei_growth.py b/src/pybamm/models/submodels/interface/sei/sei_growth.py
@@ -137,6 +137,15 @@ def get_coupled_variables(self, variables):
             # Scott Marquis thesis (eq. 5.94)
             eta_inner = delta_phi - phase_param.U_inner
             j_sei = (eta_inner < 0) * phase_param.kappa_inner * eta_inner / L_sei_inner
+        elif SEI_option == "tunnelling limited":  #
+            # This comes from eq.25 in Tang, M., Lu, S. and Newman, J., 2012.
+            # Experimental and theoretical investigation of solid-electrolyte-interphase formation mechanisms on glassy carbon.
+            # Journal of The Electrochemical Society, 159(11), p.A1775.
+            j_sei = (
+                -phase_param.j0_sei
+                * pybamm.exp(-alpha_SEI * F_RT * delta_phi)
+                * pybamm.exp(-phase_param.beta_tunnelling * L_sei_inner)
+            )
 
         elif SEI_option == "Kolzenberg2020":
             # Equation 19 in
@@ -178,6 +187,7 @@ def get_coupled_variables(self, variables):
             #  j = -F * c_0* k_exp() / (1 + L * k_exp() / D)
             #  c_ec = c_0 - L * k_exp() / D / (1 + L * k_exp() / D)
             #       = c_0 / (1 + L * k_exp() / D)
+            eta_SEI = delta_phi
             k_exp = phase_param.k_sei * pybamm.exp(-alpha_SEI * F_RT * eta_SEI)
             L_over_D = L_sei / phase_param.D_ec
             c_0 = phase_param.c_ec_0

diff --git a/src/pybamm/parameters/lithium_ion_parameters.py b/src/pybamm/parameters/lithium_ion_parameters.py
@@ -428,6 +428,9 @@ def _set_parameters(self):
         self.L_tunneling = pybamm.Parameter(
             f"{pref}tunneling distance for electrons [m]"
         )
+
+        self.beta_tunnelling = pybamm.Parameter(f"{pref}Tunneling barrier factor [m-1]")
+
         self.L_sei_0 = self.L_inner_0 + self.L_outer_0
         self.E_sei = pybamm.Parameter(f"{pref}SEI growth activation energy [J.mol-1]")
         self.alpha_SEI = pybamm.Parameter(f"{pref}SEI growth transfer coefficient")