1. The importance of surface for fine powder
Paul C. Hiemenz, “Principles of colloid and surface,”
Advanced Electronic Ceramics I (2004)
The importance of surface for fine powder
Paul C. Hiemenz, “Principles of colloid and surface,”
Advanced Electronic Ceramics I (2004)
2. Diameter of irregular-shape particle
Martin diameter: the length of line which bisects the projected
area of a particle
a 21/2a 2a 23/2a 4a
The use of graticule to estimate a characteristic
dimension of an irregular particle
Paul C. Hiemenz, “Principles of colloid and surface,”
Advanced Electronic Ceramics I (2004)
Diameter of asymmetrical particle
Prolate ellipsoid (a>b) Oblate ellipsoid (a>b)
a: radius of ellipsoid measured along the axis of rotation
b: radius measured in the equatorial plane
Paul C. Hiemenz, “Principles of colloid and surface,”
Advanced Electronic Ceramics I (2004)
3. Mean diameter
Poly-disperse
Mono-disperse
3
1 2
2 2 2
Advanced Electronic Ceramics I (2004)
Mean diameter
dn < ds < dv
(meaning)
- as increasing the polydispersity of powder
(or as becoming the size distribution more wide),
the square and cubic terms increase to a larger extent
- mean value increment in ds and dv mainly by the large particle
- the difference between the above mean diameters increases
at the polydisperse powders
- indication of the polydispersity
Advanced Electronic Ceramics I (2004)
4. Determination of Mean diameter by SEM and TEM: Discussion
Advanced Electronic Ceramics I (2004)
Particle-size distribution
Mode : top
Median L bisect the area of the curve
T. Allen, “Particle size measurement,”
Advanced Electronic Ceramics I (2004)
5. Sedimentation
Fg: gravitational force
Sedimentation of a particle in a fluid
Fb: buoyant force
the net force for the particle
ρ1: density of fluid
Fnet = Fg - Fb = V(ρ2 - ρ1)g
ρ2: density of particle
Fv = f v Fv: viscous force
(the viscous force is proportional to f: friction factor
the velocity of particle) (kg/sec.)
m: the mass of particle
at stationary state (= ρ2V)
V(ρ2 - ρ1)g = f v
m (1- ρ1/ ρ2 )g =f v
v : measurement ⇒ m/f can be attained
- f determination from (a) calculation or (b) experiment such as
diffusion study
Advanced Electronic Ceramics I (2004)
Stoke’s equation 1
(assumption)
1. Laminar flow(small Reynolds number)
2. Spherical shape
3. No solvation
velocity of any volume element passing
sphere is a function of both time and
location (flow stream line function)
- derived by Stokes in 1850
Viscous force on a moving particle with a velocity(v) in a fluid with a
viscosity(η)
Fv = 6π η R v R: the radius of particle
the friction factor for a spherical particle is given by
f = 6π η R
Advanced Electronic Ceramics I (2004)
6. Stoke’s equation 2
Advanced Electronic Ceramics I (2004)
Stoke’s equation 3
The problems
in Stoke’s analysis
1. Solvation increases R
2. In anisotropic particle,
the longer dimension
rather than shorter one
plays the role of increasing R
3. Needs a modification
in a turbulent region
Advanced Electronic Ceramics I (2004)
7. Photo-sedimentation
The use of white light
t=0 t = t1
h
Narrow
horizontal Photocell
beam of
parallel
light
Intensity increases as increasing sedimentation time
1/2 1/2
9ηv 9ηh
R= = Intensity
2(ρ2- ρ1)g 2(ρ2- ρ1) g t ⇒ particle-size distribution
Advanced Electronic Ceramics I (2004)
Photo-sedimentation: example
SA-CP3 (Centrifugal Particle Size Analyzer)
The Shimadzu SA-CP3 is a particle size analyzer which
combines particle sedimentation with photometric
detection.
Particle sizes can be measured over a very wide range
because sample particles are settled in any of four
modes: The Gravitational sedimentation mode, the
Centrifugal sedimentation mode, the Multi mode
(Combining gravitational sedimentation and centrifugal
sedimentation), and the Centrifugal lift mode. Operation in
any mode is quite easy through a dialogue with the CRT.
Why centrifugal?
- increase the sedimentation speed of fine particles
by several orders of magnitude.
- greatly moderates the effect of Brownian motion.
♦ Typical measuring range : 0.02 - 500 µm (depending on particle density,
dispersant density, viscosity)
♦ Sample Concentration in Dispersant: < .01 wt% (Differs with sample)
♦ Light Source: Halogen lamp, 6V, 10W
♦ Photo sensor: Silicon photocell
http://www.ssi.shimadzu.com/
Advanced Electronic Ceramics I (2004)
8. X-ray sedimentation
The use of X-ray
I: Resultant X-ray density
Io: Incident X-ray density
B: constant
I=Ioexp(-BC)
C: concentration of powder in the beam
D=log (I/Io) D: X-ray density
Advanced Electronic Ceramics I (2004)
Sedimentation
Possible errors in sedimentation technique
1. Hindered settling due to particle interactions
2. The tendency of fine particles to be pulled along behind large ones
3. Agglomeration caused by Brownian motion
Typical time for the 1 cm sedimentation (alumina in water)
1. 1 min for 10 µm alumina
2. 2h for 1 µm alumina
Disadvantages
1. Requires the densities of materials
2. Not good for emulsion where the material does not settle
3. Not good for very dense material that settles too quickly
4. Need to keep constant temperature for constant viscosity of medium
Advanced Electronic Ceramics I (2004)
9. Particle shape analyzer Operating Principle
A sample dispersion is aspirated using a
pipette and drawn into an agitation
chamber where it is maintained in
suspension. From here it is injected via a
jet nozzle into the Flow Cell, where it is
sandwiched between two sheath flows
through hydrodynamic effects. The
combination of this hydrodynamic process
and the laminar flow created results in a
very thin flat flow approximately 2 microns
thick. This monolayered and dispersed
particle flow is presented to the camera for
image analysis, an approach that ensures
all particles are in focus.
The cell is illuminated with a stroboscope and images of the particles are captured every
1/30th of a second. These are processed in real time through digitization, edge highlighting,
binarization, edge extraction, edge tracing and image storage. Image analysis allows
calculation of the area and perimeter of each captured particle image, followed by
determination of particle diameter and circularity. The circularity and diameter data allow the
numeric classification of particle shape.
Once the measurement is complete the particle size and circularity data are displayed in
graphical and tabular formats. A typical measurement is completed in around 5 minutes.
http://www.malvern.co.uk/Laboratory/fpiaop.htm
Advanced Electronic Ceramics I (2004)
Particle shape analyzer
http://www.malvern.co.uk/
Advanced Electronic Ceramics I (2004)
10. Laser diffraction
d > 50 µm d < 50 µm
Fraunhofer approximation Mie approximation
diffraction of light outside of the cross takes into account both diffraction
section of the beam and diffusion of the light
around the particle in its medium.
Consideration of complex
Mie scattering becomes possible
due to the progress in computer
Figure is from
http://www.cilas.com/englais3/html/angranul/theory/mie.htm
Advanced Electronic Ceramics I (2004)
Laser diffraction: example
http://www.beckmancoulter.com/
Advanced Electronic Ceramics I (2004)
11. Laser diffraction: example
http://www.ssi.shimadzu.com/products/5_test_and_physical_measurement/sald2001.html
Advanced Electronic Ceramics I (2004)
Photon Correlation Spectroscopy(Light Intensity Fluctuation)
The PCS method consists in determining the velocity distribution of particles
movement by measuring dynamic fluctuations of intensity of scattered light. The
disperse particles or macromolecules suspended in a liquid medium undergo
Browning motion which causes the fluctuations of the local concentration of the
particles, resulting in local inhomogeneities of the refractive index. This in turn
results in fluctuations of intensity of the scattered light. The line width of the light
scattered spectrum Γ (defined as the half-width at half-maximum) is proportional
to the diffusion coefficient of the particles D:
where
n is the refractive index of the medium, λ the laser wavelength, and Θ the
scattering angle. With the assumption that the particles are spherical and non-
interacting, the mean radius is obtained from the Stokes-Einstein equation:
where kB is the Boltzmann constant, T the temperature, and η the shear
viscosity of the solvent.
Www.photocor.com
Advanced Electronic Ceramics I (2004)
