CHEM-E4106 - Electrochemistry D, Lecture, 9.1.2023-21.2.2023

A                 area; parameter in the Debye-Hückel theory; constant in Eq. (7.61)

a                 activity; ionic radius; Tafel slope

a_±                mean activity of the electrolyte

B                 parameter in the Debye-Hückel theory

b                 Tafel slope

C                capacitance; dimensionless concentration c/c₀

C_d               capacitance of the diffuse layer

C_dl              double layer capacitance

C_p               pseudo capacitance

C₂               capacitance of the inner layer

c                 molar concentration

c₀                initial concentration

c^b                bulk concentration (typically equal to c₀)

D                diffusion coefficient; dissipation coefficient

D_±               diffusion coefficient of the electrolyte

d                 width of the channel (Fig 7.14)

E                 energy; cell potential; strength of the leectric field (chapter 3.1)

E⁰               standard potential

E^0’              conditional potential (formal potential)

E_1/2             half wave potential

E_eq              equilibrium potential of the electrode

E_i                initial potential of the linear potential sweep

E_s               switching potential of the linear potential sweep

E_diss            dissipated energy

E_stored         stored energy

E_f                Fermi energy

e                 elementary charge, 1.602×10⁻¹⁹ C

e⁻                electron

F                 Faraday constant, 96485 C mol⁻¹

f                  F/RT; activity coefficient on the mole fraction scale; friction coefficient; frequency

f₀                 charachteristic frequency of the quartz crystal

G                Gibbs free energy

$\Delta G_a^{\ddagger}$           activation energy of a reaction

H(s)            transfer function

H₀               Hammet acidity function

H₋               Hammet basicity function

h                 thickness of a membrane; 2h = height of the channel (kuva 7.14)

I                  electric current; ionic strength

I_C                capacitive current

I_f                 Faradic current

I_lim              electric current limited by diffusion

i                  current density

i₀                 exchange current density

i_d                 current density in the Cottrell experiment

i_kin              current density determined by kinetics

i_lim              current density limited by diffusion

J                 flux of the amount of substance (mol cm⁻² s⁻¹)

j                  imaginary unit, $\sqrt{-1}$

K                equilibrium constant of a reaction

K_a               association constant

K_b               boiling point elevation constant

K_d               dissociation constant

K_f                freezing point depression constant li.e. cryoscopic constant

K^w               ionic product of water, 10⁻¹⁴ M² at 25 °C

k                 reaction rate constant; Bolzmann constant

k⁰                standard rate constant of an electrochemical reaction

k_B                Boltzmann constant 1,38×10⁻²³ J K⁻¹

k_a                adsorption constant

k_d                desorption constant

k_ox               rate constant of the oxidation reaction

k_red              rate constant of the reduction reaction 

L                 inductance

l                  dimension of the electrode (Fig. (7.14))

M                molar mass

m                mass; molality

N                number of particles

N_A              Avogadro constant, 6.023×10²³ mol⁻¹

n                 amount of substance

O(s)            output function

P                 pressure; probability

p                 partial pressure

Q                electric charge

q                 amount of heat; charge density; parameter in the Bjerrum theory

q_e                electric charge in solution

q’                (adsorbed) charge of the inner layer

q_d                charge of the diffuse layer

R                 resistance; gas constant 8.314 J K⁻¹ mol⁻¹

R_ct               charge transfer resistance

R_p               pseudo resistance

r                  rreaction rate; distance in spherical coordinates, radius

S                 entropy; function of linear potential sweep in Eq. (7.23)

s                  Laplace variable

T                 thermodynamic (absolute) temperature; dimensionless time

t                  time; Hittorff transport number

t_s                 time of the switching potential

U                internal energy

U(s)            input function

u                 mobility; dummy variable in integrals

V                 volume; potential field created by a single ion

$\dot{V}$              rate of volume flow

$\overline{V}$              partial molar volume

W                work/energy

w                work per particle

v                 rate of linear flow; reaction rate; rate of potentila sweep

x                 molar fraction; reaction coordinate

Y                 admittance

y                 activity coefficient on molality scale

Z                 impedance

z                  charge number; dimensionless location variable

$\alpha$                 degree of dissociation; charge transfer coefficient

$\beta$                 charge transfer coefficient

$\Gamma$                 surface concentration; gamma function

$\Gamma$_{i (1)}            relative surface concentration of species i

$\gamma$                 surface tension

$\gamma$_i                 activity coefficient of an ion on molality scale

$\gamma$_±                mean activity coefficient on molality scale

$\delta$                 thickness of diffusion layer; integration step; phase difference between ac signals

$\varepsilon$₀                relative permittivity of space 8.854×10⁻¹² F m⁻¹

$\varepsilon$_r                relative permittivity

$\eta$                 overpotential E − E_eq; viscosity

$\eta$_a               activation overpotential

$\eta$_c               concentration overpotential

$\theta$                 exp[(nF)/(RT)(E − E^0’)]; surface coverage of hydrogen or oxygen

$\theta$_i                exp[(nF)/(RT)(E_i − E^0’)]

$\kappa$                 conductivity of solution

$\kappa$⁻¹              Debye length

$\Lambda$                molar conductivity of solution

$\lambda$_i                molar conductivity of an ion

$\lambda$                 solvent reorganization energy in the Marcus theory

$\mu$                 chemical potential

$\mu$⁰               standard chemical potential

$\tilde\mu$               electrochemical potential

$\tilde\mu^0$              standard electrochemical potential

$\nu$                 dynamic viscosity of solution

$\pi$                 osmotic pressure

$\xi$                 ratio of diffusion coefficients $\sqrt{D_{\text{O}}/D_{\text{R}}}$

$\rho$                 density of solution; charge density

$\sigma$                 constant of Warburg impedance; dimensionless sweep rate (nF)/(RT)×v

$\sigma$^m               surface charge of the electrode

$\tau$                 time constant of RC circuit t = RC, dimensionless time $\tau=\sigma t$, transition time (7.50)

$\Phi$                work funktion; osmotic coefficient

$\phi$                 galvani potential

$\phi$₀                galvani potential of the solution at the surface of the electrode

$\phi$₂                galvani potential at the interface of Helmholtz layer

$\Delta_o^w\phi^0$         standard potential of ion transfer from organic phase to water

$\varphi$                 dimensionless galvani potential (F$\phi$)/(RT); surface coverage in Chapter 9

$\psi$                outer potential; parameter in linear potential sweep, Eq (7.23)

$\ \chi$                 surface potential; dimensionless current

$\omega$                angular frequency