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.