Electrochemistry Nomenclature

The following is a guide to the symbols used in this section.

Scalars


$α_{1}$	Electrode reaction order [-]
$α_{2}$	Vacancies reaction order [-]
$α_{3}$	Electrolyte reaction order [-]
$α_{a}$	Anodic transfer coefficient [-]
$α_{c}$	Cathodic transfer coefficient [-]
$ε_{0}$	Vacuum permittivity [F/m]
$Δ G °$	Gibbs free energy of reactants and products [J/mol]
$η$	SEI surface overpotential [V]
$η_{i}$	Surface overpotential of species $i$ [V]
$κ$	Ionic conductivity [S/m] or [A/V m]
$μ_{e}$	Chemical potential of electrolyte [J/mol]
$ν_{+}$	Number of cations into which a molecule of electrolyte dissociates [-]
$\overline{c_{+}}$	Uniform/Volume average Lithium/Salt concentration in positive electrode [kmol/m³]
$\overline{c_{-}}$	Uniform/Volume average Lithium/Salt concentration in negative electrode [kmol/m³]
$\overline{x_{i n i t}}$	Volume average initial stoichiometry of negative electrode active materials [-]
$\bar{x}$	Volume average stoichiometry of negative electrode active materials [-]
$\overline{y_{i n i t}}$	Volume average initial stoichiometry of positive electrode active materials [-]
$\bar{y}$	Volume average stoichiometry of positive electrode active materials [-]
$ϕ$	Electric potential [V]
$ϕ_{s}$	Electric potential of the solid [V]
$ϕ_{l}$	Electric potential of the liquid electrolyte [V]
$σ$	Effective electrical conductivity [S/m] or [A/V m]
$σ_{0}$	Electrical conductivity [S/m] or [A/V m]
$τ$	Tortuosity, non-unity only in separator [-]
$τ_{e q}$	The characteristic timescale for equilibrium.
$C$	Double-layer capacitance [F/m²] [C/V m²]
$c$	Molar concentration of a single electrolyte [kmol/m³]
$c_{0}$	Molar concentration of solvent [kmol/m³]
$c_{i}$	Molar concentration of species $i$ [kmol/m³]
$c_{i}^{e q}$	Equilibrium molar concentration of a reactant or procuct [kmol/m³]
$c_{l}$	Molar concentration of lithium cations in electrolyte (liquid) [kmol/m³]
$c_{s}$	Molar concentration of lithium in electrode material (solid) [kmol/m³]
$c_{l, ref}$	Molar reference concentration of lithium in electrolyte [1 kmol/m³]
$c_{s, max}$	Molar concentration of lithium in saturated electrode material [kmol/m³]
$c_{i, r e f}$	Reference concentration for species $i$ [1 kmol/m³]
$C A P$	Cell capacity [C] [A s]
$D$	Effective diffusivity [m²/s]
$D_{0}$	Reference diffusivity [m²/s]
$D_{i}$	Diffusivity of species $i$ [m²/s]
$E^{0}$	Nernst Standard Potential at the reference molar concentration of unity [V]
$E_{a}$	Kinetic activation energy [J/kmol]
$E_{SEI}$	SEI activation energy [J/kmol]
$F$	Faraday’s constant [96485339.924 C/kmol]
$f$	Force [N/m³]
$f_{\pm}$	Mean molar activity coefficient of an electrolyte [-]
$γ_{i}$	Rate exponent of electrochemical species, $i$
$H e$	Henry's constant [dimensionless]
$H$	Enthalpy [J/kg]
$j$	Specific electric current [A/m²]
$j_{0}$	Exchange current density [A/m²]
$j_{n}$	SEI normal component of electric current density [A/m²]
$j_{n, l}$	Boundary specific electric current density on the fluid [A/m²]
$j_{n, s}$	Boundary specific electric current density on the solid [A/m²]
$j_{n, s, i}$	Boundary specific electric current density on the solid, for species $i$ [A/m²]
$k_{f}$	Forward reaction rate
$k_{r}$	Reverse reaction rate
$κ$	Ionic conductivity [S/m]
K	Ion mobility [m²/Vs]
$K$	Rate coefficient [equiv/s m²]
$K_{e q}$	Equilibrium constant
$K_{0}$	Reference rate constant [equiv/s m²]
$ξ$	Equilibrium concentration constant of the reaction [kg kmol^-1]
$n_{+}$	Li+ cations in positive electrode active material [kmol]
$n_{-}$	Li+ cations in negative electrode active material [kmol]
$n_{e q}$	Equivalent number of electrons per mole of reactant
$ν_{i}$	Stoichiometric coefficient of electrochemical species $i$
$ν_{e}$	Stoichiometric number of electrons
N	Number flux [1/m²s]
$N_{n, s, i}$	Molar concentration flux of species $i$ from the solid to the liquid [kmol/ m² s]
$N_{A}$	Avogadro constant 6.022136736 e²⁶[1/kmol]
$n_{p}$	Number density [1/m³]
$O C V$	Open circuit voltage [V]
$O C V_{S O C = 0}$	Open circuit voltage at SOC = 0
$O C V_{S O C = 1}$	Open circuit voltage at SOC = 1
$p_{r e f}$	Reference pressure [1.0 atm]
$q$	Elementary charge 1.602176487 e^-19[A s]
${\dot{q}}_{V}$	Volumetric heat release [W/m³]
${\dot{q}}_{A}$	Per-area heat release [W/m²]
$ρ_{i o n}$	Ionic space charge density [A s/m³]
$r_{s u r f}$	Surface sorption rate
$R_{u}$	Universal gas constant [8314.4621 J/kmol K]
$R$	Electrical resistance [ $Ω$ m²]
$R_{0}$	Reference electrical resistance of SEI [ $Ω$ m²]
$R_{SEI}$	Electrical resistance of SEI [ $Ω$ m²]
$s$	Entropy
$s_{+}$	Stoichiometric coefficient of cation in electrode reaction [-]
$s_{0}$	Stoichiometric coefficient of solvent in electrode reaction [-]

$S_{c_{i}}$	Electrochemical species source term
$S_{E s t a t}$	Electric charge density
$S O C$	State of charge. $S O C \in [0, 1]$ under standard operation conditions. [-]
$T$	Temperature [K]
$t$	time [s]
${t_{+}}^{0}$	Transference number of cations with respect to the velocity of the solvent species [-]
$u_{i}$	Mobility of species $i$ [m²kmol /J s]
$U$	Potential difference
$U_{+} (y)$	Relative galvanic equilibrium potential of positive active electrode material [V]
$U_{-} (y)$	Relative galvanic equilibrium potential of negative active electrode material [V]
$U_{e q}$	Relative galvanic equilibrium potential of active electrode material [V]
$v$	Velocity [m²/s]
$V_{+}$	Volume of positive electrode active material [m³]
$V_{-}$	Volume of negative electrode active material [m³]
$W_{i}$	Molar mass of species $i$ [kg/kmol]
$χ$	Porosity, non-unity only in separator [-]
$z_{+}$	Charge number of cation [-]
$z_{i}$	Charge number of species $i$ [i]
$S E I$	Solid electrolyte interface

Tensors or Column Vectors


$a$	Normal vector for area [m²]
$E$	Electric field $- \nabla ϕ$ [N/C] or [V/m]
$J$	Electric current density [A/m²]
$N_{+}$	Lithium (cation) molar flux [kmol/m²s]
$N_{i}$	Molar flux [kmol/m²s]
$N_{P}$	Number flux [number/m²s]
$v$	Velocity [m/s]

Cartesian Vectors


$n_{l}$	Normal vector pointing outwards from liquid region [-]
$n_{s}$	Normal vector pointing outwards from solid region [-]