2.5 The Nature of the Electron Conductor/Solution Interface
17
in contact with the electrolyte solution can be charged, and the ions bearing the
opposite charge may accumulate at the surface. The charged metal and the ion layer
in the solution together make an electrical double layer. It is straightforward that the
modification of the charge on the surface of the metal leads to a redistribution of the
ions near the metal/solution interface. Such an interface behaves in a similar way as an
electrostatic capacitor, and the ionic conductor/electrolyte solution interface always
exhibits capacitive properties. Later, Gouy and Chapman completed Helmholtz’s
theory by assuming a distribution of ions in the solution near a charged surface in
accord with the thermal fluctuations, hence modifying the parallel-plate model and
introducing the concept of the diffuse double layer. This assumption led again to the
Poisson–Boltzmann problem, with the difference as compared to the environment
of a dissolved ion that the spherical ion distribution turns into a planar one. This
consideration could explain that the differential capacitance of the interface is not
constant but depends on the surface density of the charge carriers already accumulated
therein. However, another limitation came from the fact that the medium was treated
as a continuum. The proper constraint was set later by Stern (1924) by defining the
closest approach of an ion to the surface as the radius of this ion. The introduction
of the distance of closest approach resulted in a maximum of the capacitance of the
interface, hence eliminating a weakness of earlier theories.
The picture on a metal/solution interface can be further complicated if specific
adsorption of ions at the solid surface is also assumed, which shifts the purely physical view on the interface towards a chemically more realistic contemplation. The
goal here is not the exact quantitative treatment of all related phenomena (that can be
found elsewhere; see, e.g., Chap. 2 of [3], Chap. 3 of [12] and [13]). Instead, a reliable qualitative picture is offered that is suitable to elucidate the capacitance-related
interfacial phenomena. For this purpose, the scheme in Fig. 2.2 is recommended.
A detailed description of the electrochemical double layer involves the following
concepts: the inner Helmholtz plane is defined at the centre of the strongly adsorbed
non-hydrated ions. The outer Helmholtz plane lies at the centre of hydrated ions at the
closest approach to the metal surface while the hydration shell is intact. The diffuse
double layer ranges to a distance from the metal surface where the concentration
of the cations and anions is equal to their bulk concentration and the influence of
the charged surface decays. The characteristic thickness of the diffuse double layer
(χ ) is inversely proportional to the square root of the electrolyte concentration. It is
practically negligible at large electrolyte concentrations (if c > 0.1 mol dm
−3 , χ <
1 nm) but can range to several hundred nanometers if c < 10
−6 mol dm
−3 .
It is a key question in the study of the electrical double layer of electrodes at which
potential the charge of the surface becomes zero. This potential of zero charge (E pzc )
can be established mostly indirectly, either from the minimum of the differential
capacitance as a function of the electrode potential, from the maximum of the surface
tension of a liquid metal or from sensitive chronocoulometric measurements carried
out during the immersion of the metal into the electrolyte solution under potentiostatic
control. However, regardless of the exact value of E pzc , in experiments with varying
potential the capacitance effects have to be taken into account. A positive change in
electrode potential leads to a positive double layer charging current and vice versa.
17
in contact with the electrolyte solution can be charged, and the ions bearing the
opposite charge may accumulate at the surface. The charged metal and the ion layer
in the solution together make an electrical double layer. It is straightforward that the
modification of the charge on the surface of the metal leads to a redistribution of the
ions near the metal/solution interface. Such an interface behaves in a similar way as an
electrostatic capacitor, and the ionic conductor/electrolyte solution interface always
exhibits capacitive properties. Later, Gouy and Chapman completed Helmholtz’s
theory by assuming a distribution of ions in the solution near a charged surface in
accord with the thermal fluctuations, hence modifying the parallel-plate model and
introducing the concept of the diffuse double layer. This assumption led again to the
Poisson–Boltzmann problem, with the difference as compared to the environment
of a dissolved ion that the spherical ion distribution turns into a planar one. This
consideration could explain that the differential capacitance of the interface is not
constant but depends on the surface density of the charge carriers already accumulated
therein. However, another limitation came from the fact that the medium was treated
as a continuum. The proper constraint was set later by Stern (1924) by defining the
closest approach of an ion to the surface as the radius of this ion. The introduction
of the distance of closest approach resulted in a maximum of the capacitance of the
interface, hence eliminating a weakness of earlier theories.
The picture on a metal/solution interface can be further complicated if specific
adsorption of ions at the solid surface is also assumed, which shifts the purely physical view on the interface towards a chemically more realistic contemplation. The
goal here is not the exact quantitative treatment of all related phenomena (that can be
found elsewhere; see, e.g., Chap. 2 of [3], Chap. 3 of [12] and [13]). Instead, a reliable qualitative picture is offered that is suitable to elucidate the capacitance-related
interfacial phenomena. For this purpose, the scheme in Fig. 2.2 is recommended.
A detailed description of the electrochemical double layer involves the following
concepts: the inner Helmholtz plane is defined at the centre of the strongly adsorbed
non-hydrated ions. The outer Helmholtz plane lies at the centre of hydrated ions at the
closest approach to the metal surface while the hydration shell is intact. The diffuse
double layer ranges to a distance from the metal surface where the concentration
of the cations and anions is equal to their bulk concentration and the influence of
the charged surface decays. The characteristic thickness of the diffuse double layer
(χ ) is inversely proportional to the square root of the electrolyte concentration. It is
practically negligible at large electrolyte concentrations (if c > 0.1 mol dm
−3 , χ <
1 nm) but can range to several hundred nanometers if c < 10
−6 mol dm
−3 .
It is a key question in the study of the electrical double layer of electrodes at which
potential the charge of the surface becomes zero. This potential of zero charge (E pzc )
can be established mostly indirectly, either from the minimum of the differential
capacitance as a function of the electrode potential, from the maximum of the surface
tension of a liquid metal or from sensitive chronocoulometric measurements carried
out during the immersion of the metal into the electrolyte solution under potentiostatic
control. However, regardless of the exact value of E pzc , in experiments with varying
potential the capacitance effects have to be taken into account. A positive change in
electrode potential leads to a positive double layer charging current and vice versa.