Surface Charge

Surface Charge

As before

= −

= +

Stern

layer Diffuse layer

Stern

layer Diffuse layer

Langmuir adsorption can be used to describe the adsorption in the Stern layer

= 1 +

= ℎ

−

From the capacitor theory

= (Ψ − Ψ )

= 1 +

÷ø ç ö

è - æ Y

= kT

kTn ze ^st

dl 8e ₀ sinh 2

s

• When an electric field is applied across an electrolyte, charged particles suspended in the electrolyte are attracted towards the electrode of

opposite charge.

• Viscous forces acting on the particles tend to oppose this movement.

• When equilibrium is reached between these two opposing forces, the particles move with constant velocity.

• The velocity of a particle in an electric field is commonly referred to as its Electrophoretic mobility.

Electrokinetic Phenomena

+ + -

-

x

dx

L

Forces acting on the layer - Electrical force

- Viscous drag

In steady state, two forces balance

= −

=

Poisson Eq. = − Ψ

− Ψ

= Integrating

− Ψ

= +

→ ∞ Ψ

→ 0, → 0 ∴ . = 0

Integrating again

− Ψ = +

= 0

Close to the surface (xà 0)

= ℎ ℎ

zeta potential (electrokinetic potential)

Electroosmosis

V

Boundary Condition

= 0 ℎ = 0 ℎ

= −

. . − − Ψ = Ψ

Far from the surface Ψ = 0

=

Velocity of bulk fluid relative to surface

may have different values close to surface

= Ψ

L

Fluid flow à convection current Potential Diff. à conduction current

=

= 4 − : .

Convection current

Streaming Potential

ⓥ

Porous plug (packed bed) applied pressure

P

｝

Equal at steady state

= − Ψ: .

r R

R: radius of pores in plug

= 2

Ohm’s Law =

= :

Conduction current

Solving

= Restriction

i) laminar flow

ii) R >> double layer thickness

iii) surface conductance effects negligible ( ≫ 1)

Electrophoresis

Charged particles under an electric field experience three forces

- Electrostatic Coulomb force - Fluid drag force

- Retardation force due to the charges in the double layer moving in opposite direction - Relaxation effect: distortion of

double layer (center of + charge and – charge do not coincide)

Two extreme cases:

(1) Double layer is thin compared to particle size:

(2) Double layer is very thick compared to particle size:

( ≫ 1)

( < 0.1)

1)

And spherical particles can be treated as a point charge At steady state, electrostatic force=viscous drag

= = 6

q Ψ = 4

r

Potential close to the surface:

= 4 :

= 4

4 = 6

= 4

6 = 2

3 ̈ .

= : ℎ

for = 0.1 if = 0.01

= 10

→ : 10 M for 1: 1 electrolyte

Ex) calculate when = 10 / in water at 20^oC

= 0.01 1 = 1 g

cm = 0.1

=3 2 =

3(0.01 × 0.1)(10 )

2(80)(8.85 × 10 ) =

= 2.11 × 10

May not be applicable to particle electrophoresis in aqueous media

2) > 200

Viscous drag

Electrostatic force

Treatment is the same as electroosmosis

= : ℎ .

=

= : . = < 0.1

= 1 > 200 When is large, the double layer is effectively large,

and may be treated as such.

Mobility is independent of size and shape

Relaxation effect

=

∆ = 3 −

: : :

: .