Electrokinetic TheoryElectrokinetic TheoryStudy of moving charged particles and their interactions with electric fields.

4 general types of phenomenon

Electrophoresisapplying a field moves a charged particle

Sedimentation potentialopposite effect: moving particles createthe field

Electro-osmosismovement of a liquid (containing aqueousions) with respect to a charged surfacein a field.

Streaming Potentialopposite effect: the moving liquid nowcreates the field

What can we measure?

Mobility (u): how fast the particle moves(v) in an applied field, E. u=v/E

Need to relate this to properties of thecolloidal particles: charge, surface potential,and size.

s

s

s

visel

R6q

u

R6qE

v

Rv6fvqE

FF

For a point particle q=ze

For a colloid though, a large particle does not act like a point particle, so wemust consider the surface potential.

Zeta Potential

Potential at the surface of shear between charged surface and theliquid layer

We assume that and the Stern Potential are approximately the same

static moving

No longer are we concerned with asimple surface either: we assume thatthe charged particles are spheres

Rs smallHuckel limit

Rs largeHelmholtz-Smoluchowskilimit

Huckel Limit (RS small)(see Hiemenz and Rajagopalan)

Want a relationship between q and A general expression for the electricfield is given by Coulomb’s law:

sR6q

u

32

u

Since...HuckelEquation

valid for RS < 0.1

2elecr4

qE

s

ss

ss

R4q

)R1(R4q

)/1R(4q

R4q

Helmholtz-Smoluchowski Equation (RS large)

2

2

2

2

2

2

visel

2

2

vis

xdxx

vis

dxx

dxx

x

x

dxd

E-dx

vddxd

-*

Adx*EFF

dxdx

vdAF

dxdv

dxdv

AF

dxdv

AFdxdv

AF

Ev

u

Ev

dE-dv

0C,Cdxd

E-dxdv

0

0

v

Helmholtz-Smoluchowski Equation

valid for RS > 100

Henry’s Equation

9696

)1(96

13

48

5

161)(

)1(330

2

75

2

9

2

3)(

R)(3

2u

65

432

32

S

f

or

f

f

Assumptions•spherical particles•low field conditions (D-H approximation)•non-conducting particles•double layer undistorted by flow (relaxation effect)

+E +-

Surface Charge and Zeta Potential

)1( SS RR4q

Recall from our discussion of the Huckellimit that...

Again…•spherical particles•low field limit

Experimental Techniques

Particle Electrophoresis

Problem Solution

Small Particles cannotbe seen (e.g. proteins)

Adsorb them onsomething else

Brownian motion Do lots of runs toaverage out error

Sedimentation Do experiment inabsence of field

Convection effects Thermostat and lowcurrent densities

Electro-osmotic effects can also causedifficulties in interpretation.