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The measurement and interpretation of electric potentials from a physico-chemical point of view

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Abstract

This paper gives a brief account of some fundamental thermodynamic and electrostatic aspects of electrodes in solutions, with special reference to electrode potentials. Different types of potential should be distinguished; their operational definiteness is discussed. Formulas are given for charge, potential and capacity of a diffuse electrical double layer at a phase boundary. The applicability limits as well as possible modifications of the diffuse theory are discussed. It appears that the measurable total double layer capacity under given conditions can be represented by a diffuse and a non-diffuse capacity in series, where the salt content of the solution determines which of these predominates. Although the theory is presented in terms of electrode properties, it is much more generally applicable, e.g. in the field of the stability of colloids, or membrane performance. A short discussion on liquid junction potentials, glass electrode potentials and electrokinetic potentials is also included.

Sommaire

Un bref compte rendu donne un aperçu sur quelques propriétés fondamentales thermodynamiques et électrostatiques d'électrodes immergées dans une solution, avec référence particulière aux potentiels des électrodes. Une distinction est faite entre différents types de potentiels et la définition de leurs différents modes opérationnels est discutée. Des formules sont données exprimant la charge, le potentiel et la capacité d'une double zône électrique diffuse à la limite des milieux. Les possibilités des différentes applications de cette théorie ainsi que ses modifications possibles sont envisagées. Il apparaît que la capacité totale mesurable de la double zône électrique peut, sous certaines conditions, être exprimée par une capacité en série, diffuse ou localisée, selon le degré de concentration saline de la solution. Quoique cette théorie soit exposée en termes de propriétés d'électrodes, elle peut s'appliquer dans un sens beaucoup plus large, par exemple à l'étude de la stabilité des colloïdes ou à celle de la qualité des membranes. Les potentiels à l'interface des liquides, des électrodes en verre et de l'électrocinétique sont brièvement commentés.

Zusammenfassung

Dieser Artikel gibt einen kurzen Bericht über einige grundlegende thermodynamische und elektrostatische Aspekte von Elektroden in Lösungen unter besonderer Berücksichtigung der Elektrodenpotentiale. Verschiedene Potentialarten sollten unterschieden werden; Möglichkeiten ihrer praktischen Bestimmung werden besprochen. Es werden Formeln angegeben für Ladung, Potential und Kapazität einer diffusen elektrischen Doppelschicht an einer Phasengrenze. Die Grenzen der Anwendbarkeit und ebenso mögliche Einschränkungen dieser Theorie werden besprochen. Es zeigt sich, daß unter gewissen Bedingungen die meßbare Gesamtkapazität der Doppelschicht als eine Reihenschaltung aus einer diffusen und nicht-diffusen Kapazität aufgefaßt werden kann, wobei der Salzgehalt der Lösung den jeweilig überwiegenden Anteil bestimmt. Obwohl die Theorie in der Form von Elektrodeneigenschaften gegeben ist, ist sie doch allgemeiner anwendbar, z.B. auf dem Gebiet der Stabilität von Kolloiden oder der Membranvorgänge. Potentiale an Flüssigkeitsgrenzen, bei Glaselektroden und elektrokinetische Potentiale werden kurz diskutiert.

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Abbreviations

a :

radius of spherical particle or spherical electrode

a i :

activity

c :

concentration

C :

differential capacity =dσ/dψ

D :

part of the electrode potential attributable to free charges

e :

elementary charge

E :

potential:E s-applied potential (polarizable electrode),E o-standard potential,E diff-liquid junction or diffusion potential,E m-membrane potential

F :

Faraday

i :

subscript denotes given ion

k:

Boltzmann-constant

K :

integral capacity=σ/ψ

n :

number of dipoles per cm2

n i :

number of ionsi per cm3

Q :

charge

r :

distance from (curved) interface

R :

gas constant

t :

transport number

T :

absolute temperature

w i :

work required to bring ioni from infinity to the place wherew i is measured

x :

distance from (flat) interface

z i :

valency, sign included

α:

real potential=z μi+zieχ

α:

(superscript), denotes a given phase

β:

(superscript), denotes a given phase

γ:

interfacial tension

δ:

thickness of molecular condensor

δ:

(subscript), denotes value of named magnitude forx=δ

ε:

dielectric constant

ζ:

electrokinetic potential

η:

viscosity

ηi :

total or electrochemical potential

ξ:

\(\kappa \left( {\frac{{4\pi e^2 \sum\limits_i {n_i } \left( \infty \right)z_i ^2 }}{{\varepsilon kT}}} \right)^{\frac{1}{2}} \)

μ:

dipole moment

μi :

thermodynamic potential

ρ:

space charge density

σ:

surface charge

ϕ:

Galvani- or inner potential

Φ:

specific adsorption potential=non Coulombic contribution tow i

χ:

surface potential jump

ψ:

Volta. or outer potential. Variable potential in the double layer

Δ:

difference

αΔβ :

value of named magnitude in phase β minus value in phase α

∇2 :

Nabla square or Laplace-operator

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  1. Laboratory for Physical and Colloid Chemistry, Agricultural University, De Dreyen 6, Wageningen, Netherlands

    J. Lyklema

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Based on an invited paper presented at the 5th International Conference on Medical Electronics, Liège, July 1963.

The russian translation of the abstract to this paper will be printed in a loose-leaf insert to be distributed with the next issue of the Journal.

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Lyklema, J. The measurement and interpretation of electric potentials from a physico-chemical point of view. Med. Electron. Biol. Engng 2, 265–280 (1964). https://doi.org/10.1007/BF02474623

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