The document summarizes the Stern model of the electrical double layer at electrode-electrolyte interfaces. The Stern model proposes that the double layer consists of two parts - an inner compact layer where ions are firmly adsorbed, and an outer diffuse layer where ions are scattered in solution. The potential drops linearly within the compact layer and exponentially within the diffuse layer. The Stern model implies that there are two potential drops and that the interface can be represented as two capacitors in series. At high electrolyte concentrations, the diffuse layer is compressed and the interface capacity is equal to the compact layer capacity alone.

1. Physical Chemistry of Soils
Department of Agril. Chemistry and Soil Science
Bidhan Chandra Krishi Viswavidyalaya,
Prof. P.K. Mani
ACSS-553
E-mail: pabitramani@gmail.com,

2. The Stern Model
The Helmholtz-Perrin thesis of a layer of ions in contact
with the electrode and the Gouy-Chapman antithesis of
the ions' being scattered out in solution in thermal disarray
suggest the synthesis of having some ions stuck at the
electrode and the others scattered in cloud like fashion.
This synthesis was made by Stern.
The simplest version of the Stern
theory consists in eliminating the
point-charge approximation of the
diffuse-layer theory. This is done in
exactly the same way (Fig. 7.69) as
in the theory of ion-ion interactions ;
the ion-centers are taken as not
coming closer than a certain
critical distance a from the
electrode

3.  Next to the electrode we have a region of high electric field and low
dielectric constant (εr value ca. 6) with a row of firmly held counter ions.
Beyond that there is an ionic atmosphere (the diffuse layer) where there is
a balance between the ordering electrostatic force and disordering
thermal motions. The dielectric constant increases rapidly with distance in
this region.
 The electrical potential varies linearly with distance (ca.hydrated ion radius)
within the inner compact layer and decreases in an approximate exponential
manner with distance within the diffuse layer, decaying to zero in the bulk soln.
Stern model of the interface region

4. A Consequence of the Stern Picture: Two Potential Drops across an
Electrified Interface
Under all conditions, the interface as a whole (the electrode side taken
along with the electrolyte side) is electrically neutral-the net charge
density qM on the electrode must be equal in magnitude and opposite in sign
to the net charge density qS on the solution side, i.e., -qM = qs . But,
according to the Stern picture, the charge qs on the solution is partially stuck
(the Helmholtz-Perrin charge qH) to the electrode and the remainder qG is
diffusely spread out (in Gouy-Chapman style) in the solution, i.e.,
The potential variation according to the Stern model.

5. There are therefore two regions of charge separation. The first region
is from the electrode to the Helmholtz plane (the plane defined by the
locus of centers of the stuck ions); and the second region is from this plane
of fixed charges into the heart of the solution where the net charge density
is zero.
When, however, charges are separated, potential drops result. The
Stern model implies, therefore, two potential drops, i.e.,
where ΦM and ΦH are the inner potentials at the metal and the Helmholtz
planes, and ΦB is the potential in the bulk of the solution.
Why should these two potential drops, i.e., ΦM - ΦH and ΦH - ΦB,
be distinguished?
There is an important reason. The Stern synthesis of the Helmholtz
Perrin and Gouy-Chapman models also implies a synthesis of the potential
distance relations characteristic of these two models. The Helmholtz-Perrin
model-it may be recalled -argues for a linear variation of potential with
distance; and the Gouy model, an approximately exponential potential drop).

6. Stern Model: An Electrified Interface Is Equivalent to Two Capacitors in Series
An interesting result emerges from the concept of two potential drops at an
interface. One asks: How are the potential drops affected by small changes in
the charge on the metal? In other words, what is the result of differentiating the
expression for the potential difference across the interface with respect to
charge on the metal? One obtains
In the denominator of the last term, one can replace δqM with δqd because
the total charge on the electrode is equal to the total diffuse charge, i.e.,
Now examine each term in the equation. Each term is the reciprocal of a quantity which
is of the form (Small change in charge/Small change in potential difference), i.e., it
is the reciprocal of a differential capacity.
Hence, Eq. can be rewritten thus

7. where C is the total capacity of the interface; CH is the Helmholtz-Perrin capacity,
i.e., the capacity of the region between the metal and the Helmholtz plane to
store charge; and CG is the Gouy-Chapman, or diffuse-charge, capacity.
This result is formally identical to the expression for the total capacity displayed by
two capacitors in series. The conclusion therefore is that an electrified interface
has a total differential capacity which is given by the Helmholtz and Gouy
capacities in series The most generalized concept of a capacitor is that of a
region of space capable of storing charge. Capacitors in series imply that the
regions are consecutive in space, each region accounting for only a part of the
total potential difference.
The total differential
capacity C of an electrified
interface is given by the
Helmholtz and Gouy
capacities in series.

8. What happens when the concentration nO
of the electrolyte is large?
From Eq. it can be seen that
CG becomes large, while CH
does not change. Hence, with increasing
concentration, the second term in Eq. I/CG,becomes
small compared with the first I/CH ,whereupon
and, for all practical purposes,
That is, in sufficiently concentrated solutions, the capacity of the interface is
effectively equal to the capacity of the Helmholtz region, i.e., of the parallel-
plate model.
What does this mean? It means that, if the Helmholtz and Gouy regions are
compared at sufficiently high concentrations (CG, high), most of the soln
charge is squeezed onto the Helmholtz plane, or confined in a region very
near this plane. In other words, little charge is scattered diffusely into the soln
in the Gouy-Chapman disarray.

9. But what happens if CG is low, that is, what happens at sufficiently low
concentrations? Under these conditions
This means that the electrified interface has become in effect Gouy-
Chapman-like in structure, with the solution charge scattered under the
simultaneous influence of electrical and thermal forces.

10. When specific adsorption takes place, counter-ion adsorption usually
predominates over co-ion adsorption.
It is possible, especially with polyvalent or surface-active counter-ions, for
reversal of charge to take place within the Stern layer - i.e. for ψ0 and ψd to have
opposite signs (Fig. 7.3a) (Ca+2
in –vely charged surface or PO4
3-
in Alumina
surface.
Adsorption of surface-active co-ions could create a situation n which ψd has
the same sign as ψ0 and is greater in magnitude (Figure 7.3b).
Fig. 7.3.
(a) Reversal of
charge due to
the adsorption
of surface
active or
polyvalent
counter ions.
(b) Adsorption of
surface active
co-ions

12. Stern Model:
In the stern model the double
layer is divided into two parts
with a compact layer adjacent
to the surface in which the
potential changes linearly from
Ψ0 toΨδ , as an Helmholtz
classical molecular condenser
type double layer.
 The remainder of the model
comprises a diffuse Gouy-
Chapman layer in which the
potential drops from Ψδ to Ψα
O. Stern (NL) 1943
Schematic representation of the
structure of the electric double layer
according to Stern's theory

13. Grahame Model:
Grahame (1947) refined the
Stern Model by splitting the
Stern layer into two to allow
consideration of two types of
strongly adsorbed ion or ions.
Nearest the solid surface
Grahamme recognised an Inner
Helmholtz plane (IHP) in which
the adsorbed ions lose some of
their water of hydration and an
outer Helmholtz plane (OHP)
supposed to contains normally
hydrated counter ions close
to the colloid surface.

16. The Bockris, Devanathan and Muller model (Water dipole model)
The principal feature of this model is that, because of a strong interaction between
the charged electrode and water dipoles, there is a strongly held, oriented layer
of water molecules attached to the electrode. In this layer, because of
competitive adsorption, there could also be some specifically adsorbed ions
which are possible partially solvated.
The locus of centers of these ions is the inner Helmholtz plane (IHP). Adjacent to
this layer is the layer of solvated ions, which is the locus of centers of
the hydrated ions, i.e., the outer Helmholtz plane (OHP).
Just as in the case of a primary hydration sheath surrounding an ion, the first layer
of water molecules has a strong orientation (either parallel or anti-parallel to the
electric field depending on the charge of the metal). Such a complete orientation
yields a dielectric constant of about 6 for this layer.
Next to this layer is a second layer of water molecules, somewhat disoriented
due to electrical and thermal forces (this is similar to the secondary hydration
sheath around an ion). This layer has a dielectric constant of about 30 to 40.
The succeeding layers of water molecules behave like bulk water, which has
a dielectric constant of ca. 80.

17. Water dipole model of the double layer
at an electrode/electrolyte interface,
(Bockris, Devanathan and Muller).

18. Because of difference in charge between
the diffuse layer and the solid surface,
movement of one relative to the other will
cause charge separation and hence
generate a potential difference, or
alternatively, application of an electrical
potential will cause movement of one
relative to the other.
The relative movement of the solid surface
and the liquid occurs at a surface of shear.
The potential at the shear plane is known
as the zeta (ζ) potential and its value can
be determined by measurement of
electrokinetic phenomena.
Electrokinetic phenomena

19. The Zeta (ζ) Potential
When a colloidal suspension is placed in an electrical field, the colloidal particles
move in one direction (toward the positive pole). The counterions move in
another direction (toward the negative pole). The electric potential developed
at the solid–liquid interface is called the zeta (ζ) potential. The seat of the ζ
potential is the shearing plane or slipping plane between the bulk
liquid and an envelope of water moving with the particle (Figure 6.35).
Because the position of the
shearing plane is unknown,
the ζ potential represents the
electric potential at an unknown
distance from the colloidal
surface.
Van Olphen (1977)
Stated that the ζ potential is not
equal to the surface potential.
It is less than the electrochemical
potential on the colloid. Perhaps it is comparable with the Stern potential.

20. Hunter, R Foundations of Colloid Science I & II, Oxford, 1989
Electrokinetic behaviour depends on the
potential at the surface of shear between the
charged surface and the electrolyte solution.
This potential is called the electrokinetic or
ζ (zeta) potential.
The exact location of the shear plane
(which, in reality, is a region of rapidly
changing viscosity) is another unknown
feature of the electric double layer. In addition
to ions in the Stern layer, a certain amount of
solvent will probably be bound to the charged
surface and form a part of the electrokinetic
unit.
It is reasonable to suppose that the shear
plane is usually located at a small distance
further out from the surface than
the Stern plane and that ζ is, in general,
marginally smaller in magnitude than ψd

21. The Effect of Electrolytes on the Zeta (ζ) Potential
The thickness of the double layer affects the magnitude of the ζ potential.
 Increasing the electrolyte concentration in the solution usually results in
decreasing the thickness of the double layer.
 Compression of the double layer will also occur by increasing the valence of the
ions in the solution.
The ζ potential may, therefore, be expected to decrease with increasing electrolyte
concn.
It reaches a critical value at the point at which the ζ potential equals zero. This
point is called the isoelectric point. At the isoelectric point, the double layer is
very thin and particle-repulsive forces are at a minimum. At and below this point
repulsion would no longer be strong enough to prevent flocculation of particles.
The ζ potential is not a unique property of the colloid, but it depends on the
surface potential (ψ) of the clay particle.
 It is determined from the electrophoretic mobility of the suspension using the
following formula:
Ve = electrokinetic velocity, D = dielectric constant, E = emf, η = viscosity of the fluid.

22. The ζ potential, in fact, is the electrokinetic potential at the slipping plane
surface. The surface potential of the colloid is ψo. In dilute solution, the
electrokinetic potential has a value represented by ζ1. By adding salt to the
solution, the diffuse layer is suppressed and more counterions are
forced to the colloid surface within the slipping plane

23. Schematic of the electric double layer under two different electrolyte
concentrations. Colloid migration includes the ions within the slipping plane of the
colloid; Sl denotes the electric potential in dilute solution: S2 denotes the electric
potential in concentrated solution (adapted from Taylor and Ashroft, 1972)

24. At the pH, or electrolyte concentration, where the zeta potential approaches zero, the
electrophoretic mobility of the particle approaches zero. At this point, such particles would have a
tendency to flocculate. When a high-valence cation, tightly adsorbed to the surface, is in excess
of the negative charge of the colloid's surface, a phenomenon known as zeta potential reversal
takes effect. This is demonstrated in Figs. 9.9 and 9.10. Zeta potential reversal could induce
colloid dispersion, depending on the type and concentration of electrolyte present.
Fig.9.9 Influence of cation concentration
and valence on zeta potential (Taylor and
Ashroft, 1972).

28. Specific adsorption of ions : occurs because of different types of electrical
interactions between the electrodes and ions: electric field forces, image forces,
dispersion forces, and electronic or repulsive forces. When the image and
dispersion forces are larger than the electronic force, the specific adsorption of ions
occurs {physical adsorption).
However, a stronger bond could be formed by partial electron transfer between the ion
and the electrode (chemisorption); small cations (e.g., Na+
)have a strong hydration
sheath around them and are minimally adsorbed. On the
other hand, large anions (Cl-
, Br-
) have only a few water molecules in the primary
hydration sheath and since the ion-solvent interaction in this case is considerably less
than the above mentioned ion-electrode interaction, specific adsorption of the ions
occurs with some partial charge transfer of an electron.
The variation of potential with distance,
across the electrode/electrolyte interface
reveals a steep drop between the
electrode and IHP and then a small
rise between the IHP and OHP, and
thereafter the variation is similar to that
in the diffuse layer

30. b)The interaction between the test and induced charges can be calculated by
considering that the metal is replaced by an image charge (equal in
magnitude and opposite in sign to the test charge) situated as far behind
the plane corresponding to the metal surface as the test charge is in front of it.
(a)When a charge
comes near a
material, e.g., a metal,
it induces a charge
which is distributed in
a complicated way.
Image charge

32. DLVO Model

36. When the two layers overlap in a collision, the ionic concentrations change and there
is no longer equilibrium
 The osmotic pressure tends to balance the difference between the chemical potential
(ε) in solution by diffusion. This causes repulsion or attraction between the surfaces
 There is a higher ionic concentration between the surfaces than in the surrounding sol
 The osmotic pressure is proportional to the ionic concentration

37. Electrical potential of overlapping diffuse double layers between two
charged clay plates separated by a distance 2d; minimum potential ψd.
Effective thickness of unrestricted diffuse double layer shown as 1/κ
DLVO theory:
The quantitative theory to evaluate the balance of repulsive and attractive
forces when particles approach ach other was worked out by Derajguin and
Landau (1941) and independently by Verwey and Overbeek (1948) on the
basis of interacting Gouy- Chapman type electrical double layers

38. Forces of Interaction Between Particles
• Five possible forces between colloidal particles
1. Electrostatic forces of repulsion
2. Van der Waals forces of attraction
3. Born Forces of short range repulsion
4. Steric forces at the interface
5. Solvation forces due to adsorbed solvent
 Assumptions of DLVO theory:
 Dispersion is dilute.
 Only two forces act on the dispersed particles: Van der Waals force
and electrostatic force.
 The electric charge and other properties are uniformly distributed
over the solid surface.
 The distribution of the ions is determined by the electrostatic force,
Brownian motion and entropic dispersion.

39. Attractive force is due to the polarisation of one molecule caused by the
fluctuations in the charge distribution of another.
A= Hamaker Constant, depends on polarizability of the
particles and the medium separating them

41. The Balance of Repulsion & Attraction
is the sum of the electrostatic repulsion and the dispersion attraction,
DLVO theory: Notice the secondary minimum. The system
flocculates, but the aggregates are weak.
This may imply reversible flocculation.
The point of maximum repulsive energy is called the
energy barrier. Energy is required to overcome this repulsion .
The height of the barrier indicates how stable the system is .The
electrostatic stabilization is highly sensitive with respect to surface
charge(ζ~ψ~pH) and salt concentration (κ, z).

42. The fundamental feature and the DLVO theory is that this interaction, and
hence colloid stability, is determined by a combination or superposition of
the interparticle double layer repulsion energy (VR) and van der Waals
attractive energy (VA)
For charged parallel plates separated by a distance of 2d such that the diffuse
part of the double layer overlap as shown in figure, the potential energy of
repulsion (VR
) is given by

43. 1.The primary minimum indicates that the aggregated state is of the lowest-
energy condition and this is where we would expect the particles to reside .
2. The primary maximum acts as an activation barrier that must be exceeded
for aggregation to occur. As two particles come closer, they must collide with
sufficient energy to overcome the barrier provided by primary maximum.
3. The secondary minimum could be seen as a flocculated state but the
particles still have to cross the energy barrier to come into close contact at
the minimum energy state.

45. van der Waals attraction will predominate at small and at large interparticle
distances. At intermediate distances double layer repulsion may
predominate, depending on the actual values of the forces. In order to
agglomerate, two particles on a collision course must have sufficient kinetic
energy due to their velocity and mass, to “jump over” this barrier.

50. Typical Energy barrier for two charged
plates in an electrolytic medium
Variation of Energy with solute
concentration.

53. ZPC and IEP

56. Iso-electric point (IEP) is also a parameter for characterizing the surface
properties of colloids. IEP of a colloid is the pH at which the net charge on the
slip surface (plane of shear) of the electric double layer is zero, and thus the
(electrokinetic) potential equals zero.

57. The terms isoelectric point (IEP) and point of zero charge (PZC) are often used
interchangeably, although under certain circumstances, it may be productive to make the
distinction.
In systems in which H+/OH− are the interface potential-determining ions, the
point of zero charge is given in terms of pH. The pH at which the surface exhibits
a neutral net electrical charge is the point of zero charge at the surface.
Electrokinetic phenomena generally measure zeta potential, and a zero zeta
potential is interpreted as the point of zero net charge at the shear plane. This is
termed the isoelectric point. Thus, the isoelectric point is the value of pH at
which the colloidal particle remains stationary in an electrical field.
The isoelectric point is expected to be somewhat different than the point of zero
charge at the particle surface, but this difference is often ignored in practice for
so-called pristine surfaces, i.e., surfaces with no specifically adsorbed positive or
negative charges. In this context, specific adsorption is understood as
adsorption occurring in a Stern layer or chemisorption.
Thus, point of zero charge at the surface is taken as equal to isoelectric point in
the absence of specific adsorption on that surface.