Definitions and Conventions

519 words (3 min) Matthew Lacey 29 Mar 2023

Glossary

Electrode potential

Formally defined as the electromotive force (emf) of a galvanic cell comprising the electrode to be characterised and a reference electrode. Consequently, all electrode potentials must be stated versus the appropriate reference. By convention, standard electrode potentials are given relative to the standard hydrogen electrode (SHE). In lithium battery research, it is common to consider electrode potentials relative to a reference electrode comprising a lithium metal electrode immersed in a solution containing a lithium salt (Li/Li+).

Negative electrode

In a rechargeable electrochemical cell, the negative electrode is the electrode with the lower electrode potential during normal operation, and functions as the anode (i.e., is oxidised) during discharge. The use of the term “negative electrode” avoids ambiguity when distinguishing electrodes as formally it is the anode only on discharge (and hence, when charging, becomes the cathode).

Positive electrode

In a rechargeable electrochemical cell, the positive electrode is the electrode with the higher electrode potential during normal operation, and functions as the cathode (i.e., is reduced) during discharge. The use of the term “positive electrode” avoids ambiguity when distinguishing electrodes as formally it is the cathode only on discharge (and hence, when charging, becomes the anode).

Transference number

In electrolytes, the transference number, $T_i$, is defined as the number of moles of species $i$ transferred by migration, per Faraday of charge (1 F = 96485 C). The sum of the transport numbers of all ionic species in an electrolyte is 1, but $T_i$ does not have any upper or lower bounds.

Transport number

In electrolytes, the transport number, $t_i$, is defined as the fraction of the ionic current carried by species $i$. The transport number must be between 0 and 1, and the sum of the transport numbers of all ionic species in an electrolyte is 1.

Terms

Symbol Definition Units Notes
$a_i$ Thermodynamic activity of species $i$ dimensionless
$A$ Surface area cm2
$c_i$ Concentration of species $i$ mol dm-3
$C$ Capacitance F
$D_i$ Diffusion coefficient of species $i$ cm2 s-1
$E$
  1. Electrode potential
  2. Voltage
 V
$\varepsilon$ Dielectric constant dimensionless
$f$ Frequency Hz
$F$ Faraday’s constant C $F$ = 96485 C
$I$ Current A
$j$
  1. Current density
  2. Imaginary unit, $\sqrt{-1}$
  1. A cm-2
$k$
  1. Cell constant
  2. Diffusion resistance coefficient
  1. cm-1
  2. Ω s-1/2
$\mu_i$ Chemical potential of species $i$ kJ mol-1
$Ne$ Newman number dimensionless See Transference number measurement
$N_M$ MacMullin number dimensionless See MacMullin number measurement
$\omega$ Angular frequency rad s-1
$Q$ Charge C or Ah 1 Ah = 3600 C
$Q_0$ Constant phase element parameter S sn See Constant phase elements
$R$
  1. Ideal gas constant
  2. Electrical resistance
  1. J K-1 mol-1
  2. Ω
  1. $R$ = 8.314 J K-1 mol-1
$\sigma_i$ Partial conductivity of species $i$ S cm-1
$\sigma$
  1. Electrical or ionic conductivity
  2. Warburg coefficient
  1. S cm-1
  2. Ω s-1/2
  2. See Diffusion Impedance
$t_i$ Transport number of species $i$ dimensionless
$t$ time s
$T_i$ Transference number of species $i$ mol Faraday-1
$T$ Temperature K, or °C
$\tau$ Time constant s
$\theta$ Phase angle ° See Principles of EIS
$\Delta V$ Potential difference V or mV
$z_i$ Charge number of species $i$ dimensionless
$\pmb{Z}$ Electrical impedance Ω
$Z'$ Real part of the impedance Ω
$Z’'$ Imaginary part of the impedance Ω

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