Li-Ion Electric Potential Model Reference

All of the physics continua that are applied to a lithium-ion battery cell use the Li-Ion Electric Potential model which assumes a binary lithium-based electrolyte.

The transport equations for electric charge are Eqn. (4100), and Eqn. (4101). The current density, $J$ , is defined using Eqn. (4097).

Table 1. Li-Ion Electric Potential Model Reference
Theory	See Concentrated Solutions.
Provided By	[physics continuum] > Models > Optional Models
Example Node Path	Continua > Physics 1 > Models > Li-Ion Electric Potential
Requires	Using a double precision version of Simcenter STAR-CCM+: Space: Three Dimensional or Two Dimensional Time : Implicit Unsteady Material: Solid or Liquid Optional Models: Electrochemistry Electrochemistry: Li-Ion Battery Cell
Properties	Secondary Gradients. See Li-Ion Electric Potential Model Properties.
Activates	Materials	Electrical Conductivity. See Li-Ion Electric Potential Model Materials and Methods.
	Initial Conditions	Electric Potential. See Li-Ion Electric Potential Model Initial Conditions.
	Boundary Inputs	Electric Potential Specification. See Li-Ion Electric Potential Model Boundary Settings.
	Interface Inputs	See: Li-Ion Electric Potential Model Interface Settings
	Solvers	Electric Potential Electric Potential Solver Reference.
	Field Functions	See Li-Ion Electric Potential Model Field Functions.

Li-Ion Model Properties

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

On: Default value. Solves for interior and boundary types of secondary gradient.
Off: Does not solve for either type of secondary gradient.
Interior Only: Solves for the interior secondary gradients only.
Boundaries Only: Solves for the boundary secondary gradients only.

Materials and Methods

Electrical Conductivity

In transient simulations, specifies the electrical conductivity,

σ

, of the material (see Electrical Conductivity: Generalized Ohm's Law).

Method	Corresponding Method Node
Constant, Field Function Available for fluids and solids.	Electrical Conductivity > Constant, Field Function Specify $σ$ as a scalar profile.

Initial Conditions

Electric Potential: Allows you to initialize the electric potential $ϕ$ to a specified scalar profile.

Boundary Settings

Wall Boundary

Electric Potential Specification

Method	Corresponding Physics Value Nodes
Specific Electric Current Allows you to define the electric current density normal to the boundary.	Specific Electric Current Sets the specific electric current $J_{n}$ to a specified scalar profile. See Eqn. (4283).
Electric Potential Allows you to define the electric potential at the boundary according to Eqn. (4279).	Electric Potential Defines the potential $\bar{ϕ}$ in Eqn. (4279) as a scalar profile.
Electric Current Allows you to define the total electric current through the boundary.	Electric Current Sets the total electric current $I_{Γ}$ to a specified scalar profile. See Eqn. (4282).
Electric Current Density Allows you to define the electric current density at the boundary.	Electric Current Density Sets $J$ to a specified vector profile. See Eqn. (4228).
Current Voltage Characteristic Allows you to define the I-V curve at the boundary.	Current Voltage Characteristic Defines the relationship between the electric current flowing through the boundary and the electric potential at the boundary. In electrochemistry applications, you typically define this relationship using the Butler-Volmer method (see Butler-Volmer Current-Potential Characteristic). Alternatively, you can specify the I-V curve by providing tabular data. For more information, see Setting the Electric Current Potential Characteristic and Current-Voltage Characteristic Reference. Electric Potential Defines the potential $ϕ_{1}$ in Eqn. (4295) as a scalar profile.
Insulator Sets the Specific Electric Current $J_{n}$ (Eqn. (4283)) at the boundary to zero.	None
Specific Electric Power Allows you to define the electric power normal to the boundary.	Specific Electric Power Sets the specific electric power $P$ to a specified scalar profile. Simcenter STAR-CCM+ uses $P = J_{n} V$ to compute the specific electric current $J_{n}$ at the boundary, where $V$ is the electric potential (voltage). See Eqn. (4283).

Li-Ion Electric Potential Model Interface Settings

Butler-Volmer Relationship Parameters

Once the corresponding physics continua are assigned to regions, you use this node to set the parameters for the Solid Electrolyte Interface (SEI).

Resistance

R_{0}

in Eqn. (4162).

SEI Activation

E_{SEI}

in Eqn. (4162).

Capacitance

C

in Eqn. (4158).

Rate Constant

k_{0}

in Eqn. (4161).

Kinetic Activation Energy

E_{a}

in Eqn. (4161).

Maximum Concentration in Electrode

c_{s, max}

in Eqn. (4159).

Reference Concentration in Electrolyte

c_{l, ref}

in Eqn. (4159).

Anodic Transfer Coefficient

α^{a}

in Eqn. (4158).

Cathodic Transfer Coefficient

α^{c}

in Eqn. (4158).

Electrolyte Reaction Order

α^{3}

in Eqn. (4159).

Electrode Reaction Order

α^{1}

in Eqn. (4159).

Vacancies Reaction Order

α^{2}

in Eqn. (4159).

Under-Relaxation Parameter

At each iteration, governs the extent to which the newly computed solution supplants the old solution. The default value (1.0) means that no under-relaxation is used.

Electrode Equilibrium Potential

Setting	Corresponding Sub-Node
Linear This method inputs a simplified electrode equilibrium potential $U_{eq}$ . You supply the values of $U_{eq}$ for the points $y = 0$ and $y = 1$ . The values for the interval $y = [0, 1]$ are linearly interpolated. For Li-Ion cells, you can approximate the electrode equilibrium potential by a constant, for example 3.7 V for the cathode. When choosing such a setup, the driving force for discharge does not increase during the charging and the discharging process. If Prevent Electrode Depletion is deactivated, this circumstance can lead to numerical problems, where an equilibrium state cannot be attained.	Linear Electrode Equilibrium Potential Electrode Equilibrium Potential for y=0 The value of $U_{eq}$ at $y = 0$ . Electrode Equilibrium Potential for y=1 The value of $U_{eq}$ at $y = 1$ .
Tabular Uses a table as input for the electrode equilibrium potential $U_{eq}$ . The electrode equilibrium potential must decrease monotonically with increasing electrode stoichiometry $y$ .	Tabular Electrode Equilibrium Potential Properties Table The table that contains the values of $U_{eq}$ as a function of $y$ . Relative Concentration in Electrode (y) Column entry for the electrode stoichiometry $y$ . Electrode Equilibrium Potential Column entry for the electrode equilibrium potential $U_{eq}$ .

Setting

Corresponding Sub-Node

Linear: This method inputs a simplified electrode equilibrium potential $U_{eq}$ . You supply the values of $U_{eq}$ for the points $y = 0$ and $y = 1$ . The values for the interval $y = [0, 1]$ are linearly interpolated.; For Li-Ion cells, you can approximate the electrode equilibrium potential by a constant, for example 3.7 V for the cathode. When choosing such a setup, the driving force for discharge does not increase during the charging and the discharging process. If Prevent Electrode Depletion is deactivated, this circumstance can lead to numerical problems, where an equilibrium state cannot be attained.

Linear Electrode Equilibrium Potential

Electrode Equilibrium Potential for y=0: The value of $U_{eq}$ at $y = 0$ .
Electrode Equilibrium Potential for y=1: The value of $U_{eq}$ at $y = 1$ .

Tabular: Uses a table as input for the electrode equilibrium potential $U_{eq}$ . The electrode equilibrium potential must decrease monotonically with increasing electrode stoichiometry $y$ .

Tabular Electrode Equilibrium Potential Properties

Table: The table that contains the values of $U_{eq}$ as a function of $y$ .
Relative Concentration in Electrode (y): Column entry for the electrode stoichiometry $y$ .
Electrode Equilibrium Potential: Column entry for the electrode equilibrium potential $U_{eq}$ .

Projection Order

Sets the projection order that is used to compute the liquid concentration

c_{l}

and solid concentration

c_{s}

at the interface.

0th-order: Uses the corresponding cell center values. Use this method when lithium depletes or saturates.
1st-order: Uses a first order projection (default).

Prevent Electrode Depletion

When activated, corrects the user-defined equilibrium voltage curves to approach

\infty

asymptotically when

y = 0

, and

- \infty

when

y = 1

.

Activating this option ensures that a local chemical equilibrium exists under all external load conditions, where $η = 0$ in Eqn. (4160).

Prevent Electrolyte Depletion

When activated, corrects the SEI Surface Overpotential to become

η = 0

when the electrolyte depletes of salt. See Eqn. (4160).

Field Functions

Electric Potential: $ϕ$ in Eqn. (4100).
Electric Field: $E$ in Eqn. (4093).
Electric Current: $J$ in Eqn. (4093).
Electrical Conductivity: $σ$ in Eqn. (4093), and $κ_{0}$ in Eqn. (4097).
Effective Electrical Conductivity: $σ$ in Eqn. (4093), and $κ$ in Eqn. (4097).
Capacitive Specific Electric Current: The second term in Eqn. (4158).
SEI Specific Electric Current: SEI normal component of electric (Faradaic) current density, the first term in
Eqn. (4158).
SEI Surface Overpotential: $η$ in Eqn. (4160).