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.