CHEM-E4106 - Electrochemistry D, 11.01.2021-23.02.2021
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Kirja
10. List of symbols
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
Cd capacitance of the diffuse layer
Cdl double layer capacitance
Cp pseudo capacitance
C2 capacitance of the inner layer
c molar concentration
c0 initial concentration
cb 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
E0’ conditional potential (formal potential)
E1/2 half wave potential
Eeq equilibrium potential of the electrode
Ei initial potential of the linear potential sweep
Es switching potential of the linear potential sweep
Ediss dissipated energy
Estored stored energy
Ef 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 enthalpy
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
IC capacitive current
If Faradic current
Ilim electric current limited by diffusion
i current density
i0 exchange current density
id current density in the Cottrell experiment
ikin current density determined by kinetics
ilim 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
Ka association constant
Kb boiling point elevation constant
Kd dissociation constant
Kf freezing point depression constant li.e. cryoscopic constant
Kw ionic product of water, 10−14 M2 at 25 °C
k reaction rate constant; Bolzmann constant
k0 standard rate constant of an electrochemical reaction
kB Boltzmann constant 1,38×10−23 J K−1
ka adsorption constant
kd desorption constant
kox rate constant of the oxidation reaction
kred 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
NA 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
qe electric charge in solution
q’ (adsorbed) charge of the inner layer
qd charge of the diffuse layer
R resistance; gas constant 8.314 J K−1 mol−1
Rct charge transfer resistance
Rp 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
ts 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 − Eeq; viscosity
\( \eta \)a activation overpotential
\( \eta \)c concentration overpotential
\( \theta \) exp[(nF)/(RT)(E
− E0’)]; surface coverage of hydrogen or oxygen
\( \theta \)i exp[(nF)/(RT)(Ei − E0’)]
\( \kappa \) 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