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2007.10.09 7. lecture
Electrical double layer
Márta Berka és István Bányai,
University of Debrecen
Dept of Colloid and Environmental Chemistry
http://dragon.unideb.hu/~kolloid/
Adsorption of strong electrolytes from aqueous
solutions
Stoichiometric or equivalent Non-stoichiometric or ion exchange
Indifferent surface Non-indifferent surface
apolarpolar
Ashless charcoal ,
lyotropic series (Ionic
charge and size, Strength
of attraction to surface:
Al3+ > Ca2+ = Mg2+ > K+
= NH4+ > Na+. For
anions: CNS-> (PO4 ,
CO3=) > I- > NO3- > Br-
> Cl- > C2H3O2- > F- >
SO4= )
Ionic crystal
from its solution
at a specific
concentration
Electric double
layer
?? Which ion goes into the inner
layer?
Anion-, cation
Electrical double layerSurface Charge Density. When a solid emerges in a polar
solvent or an electrolyte solution, a surface charge will be
developed through one or more of the following
mechanisms:
1. Preferential adsorption of ions. Specific ion adsorption:
Surfactant ions may be specifically adsorbed.
2. Dissociation of surface charged species (proteins
COOH/COO-, NH2/NH3+)
3. Isomorphous replacement: e.g. in kaolinite, Si4+ is replaced
by Al3+ to give negative charges.
4. Accumulation or depletion of electrons at the surface.
5. Charged crystal surface: Fracturing crystals can reveal
surfaces with differing properties.
Which is the preferential adsorption of ions?
• On charged surface the ion of opposite charge
• The related ions
• The ions which form hardly soluble or dissociable
compounds with one of the ions of the lattice
• The ion of larger valences
• H+ or OH-
Example: AgCl crystal
AgNO3 or KCl solution
AgCl crystal KBr, or
KSCN solution
From NaCl, CaCl2 solution :
Ca2+
The free acid or base adsorb
stronger than the electrolytes,
because the mobilities of H +
and OH- are larger.
http://www.dur.ac.uk/sharon.cooper/lectures/colloids/interfacesweb1.html#_Toc449417608
2007.10.09 7. lecture
Surface charge
(Atkins: Physical Chemistry)
100 nm
Φ, Galvani or inner potential
ψ Volta or outer potential
κ surface potential (from the orientation of solvent molecules)
When silver iodide crystals are placed in water, a
certain amount of dissolution occurs to establish
the equilibrium:
AgI = Ag+ + I-
The concentrations of Ag+ and I- in solution are
very small because the solubility product is very
small (Ksp= aAg+ aI- =10-16). But these small
concentrations are very important because slight
shifts in the balance between cations and anions
can cause a dramatic change in the charge on the
surface of the crystals. If there are exactly equal
numbers of silver and iodide ions on the surface
then it will be “uncharged”.
Charge determining ions
σσσσ =0, p.z.c.
σσσσ <0
σσσσ >0
AgI in its own saturated solution is negatív!
cAg+=cI- =8.7x10-9 mol/l
negative
positive
pAg+NTP = 5,3
cAg+>3×10-6 mol/l
cAg+<3×10-6 mol/l
The σ, C/m2 surface charge density changes
from positive to negative or vice versa. Zero-
charged surface is defined as a point of zero
charge (p.z.c.) or zero-point charge (z.p.c.).
The
concentration
of charge
determining
ions Γ , mol/m2
2007.10.09 7. lecture
Potential-determining ionsIt seems that the iodide ions have a higher affinity for the surface and tend to be preferentially
adsorbed. In order to reduce the charge to zero it is found that the silver concentration must be
increased by adding a very small amount of silver nitrate solution about to:
cAg+<3×10-6 mol/l
The charge which is carried by surface determine its electrostatic potential. For this
reason they are called the potential-determining ions.
We can calculate the surface potential on the crystals of silver iodide by considering
the equilibrium between the surface of charged crystal and the ions in the
surrounding solution:
( )0 ln ln PZC
kTa a
zeψ = −
Where ψψψψ0 the electrostatic potential
difference (arising form the charge
bearers as ions, electrons) at the
interface (x=0), shortly surface
potential; a the activity of the ions and
aPzc the activity of the ions at zero-charged surface in the solution.
0 lnkT
aze
ψ ∆=9
0 6
8.7 1025.7 ln 150
3 10mV∆ψ
−
−
×= × = −
×
0 ( )Fσ Γ Γ+ −≈ −
surface potential of silver iodide
crystals placed in clear waterAgI in its own saturated solution is negatív!
cAg+=cI- =8.7x10-9 mol/l
The structure of the electrical double layerThe model was first put forward in the 1850's by
Helmholtz. The interactions between the ions in
solution and the electrode surface were asssumed to
be electrostatic in nature and resulted from the fact
that the electrode holds a charge density which
arises from either an excess or deficiency of
electrons at the electrode surface. In order for the
interface to remain neutral the charge held on the
electrode is balanced by the redistribution of ions
close to the electrode surface. Helmholtz's view of
this region is shown in the figure
The overall result is two layers of charge (the double layer) and a
potential drop which is confined to only this region (termed the
outer Helmholtz Plane, OHP) in solution. The model of Helmholtz
does not account for many factors such as, diffusion/ mixing in
solution, the possibility of adsorption on to the surface and the
interaction between solvent dipole moments and the electrode.
2007.10.09 7. lecture
Helmholtz model
/V
x (indiv.u.)
ΦΦΦΦ0000 surface potentialΦΦΦΦ
As simple as it is not valid
0ψψ
2007.10.09 7. lecture
Gouy-Chapman model
ΦΦΦΦ/V
x (indiv.u.)
ΦΦΦΦ0000surface potential
1/κκκκ
1/κ the thickness of the DL; κ~I1/2 ionic strength
0ψψ
( )0 exp xψ ψ κ= −
The ions would be moving about as
a result of their thermal energy
( )0 exp xψ ψ κ= −
2007.10.09 7. lecture
Stern modelIn the Stern model the ions are assumed to be able to move
in solution and so the electrostatic interactions are in
competition with Brownian motion. The result is still a
region close to the electrode surface (10 nm) containing
an excess of one type of ion (Stern layer) but now the
potential drop occurs over the region called the diffuse layer.
compact Stern layer
2007.10.09 7. lecture
Stern model, charge reversal
ΦΦΦΦ/V
x (indiv.u.)
ΦΦΦΦ0000 surface potential
ΦΦΦΦd
Stern-p.
plain of shear
ζζζζ potential
PO43-
0ψ
ψ
Stψ
compact Stern layer
2007.10.09 7. lecture
Stern model, charge increase
ΦΦΦΦ/V
x (indiv.u.)
ΦΦΦΦ0000 surface potential
ΦΦΦΦdStern-p.
plain of shear
ζζζζ potential
cationic surfactants
0ψ
Stψ
ψ
2007.10.09 7. lecture
Stern model
xSt
xSt
( )exp ( )St stx xψ ψ κ= − −
Plane of shear
κκκκ: a Debye Hückel parameter
1/ κ κ κ κ the thickness of DL
e e
ze ze
kT kTn n n n
ψ ψ− +
+ ∞ − ∞= = x
x
Finite ion size, specific ion sorption,
compact layer
The whole DL is electrically neutral.
the electrostatic interactions are in
competition with Brownian motion in
the diffuse layer
e e
ze ze
kT kTn n n n
ψ ψ− +
+ ∞ − ∞= =
the electrostatic potential
for different salt
concentrations at a fixed
surface charge of -0.2
C/m2.
The potential distribution near the
surface at different values of the
(indifferent) electrolyte concentration
for a simple Gouy-Chapman model
of the double layer. c3>c2>c1. For low
potential surfaces,the potential falls
to ψ0/e at distance 1/κ from surface.