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)

The importance of surface for fine powder

Paul C. Hiemenz, “Principles of colloid and surface,”

Advanced Electronic Ceramics I (2004)

Diameter of irregular-shape particle

Paul C. Hiemenz, “Principles of colloid and surface,”

Martin diameter: the length of line which bisects the projectedarea of a particle

a 2a 4a21/2a 23/2a

The use of graticule to estimate a characteristicdimension of an irregular particle

Advanced Electronic Ceramics I (2004)

Diameter of asymmetrical particle

Paul C. Hiemenz, “Principles of colloid and surface,”

Prolate ellipsoid (a>b) Oblate ellipsoid (a>b)

a: radius of ellipsoid measured along the axis of rotationb: radius measured in the equatorial plane

Advanced Electronic Ceramics I (2004)

Mean diameter

2 2 2

Mono-disperse

1 2 3

Poly-disperse

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 increasesat the polydisperse powders

- indication of the polydispersity

Advanced Electronic Ceramics I (2004)

Determination of Mean diameter by SEM and TEM: Discussion

Advanced Electronic Ceramics I (2004)

Particle-size distribution

Mode : topMedian L bisect the area of the curve

T. Allen, “Particle size measurement,”

Advanced Electronic Ceramics I (2004)

SedimentationSedimentation of a particle in a fluidthe net force for the particleFnet = Fg - Fb = V(ρ2 - ρ1)g

Fg: gravitational forceFb: buoyant forceρ1: density of fluidρ2: density of particle

v : measurement ⇒ m/f can be attained- f determination from (a) calculation or (b) experiment such as diffusion study

Fv: viscous forcef: friction factor(kg/sec.)

m: the mass of particle(= ρ2V)

Fv = f v(the viscous force is proportional tothe velocity of particle)

at stationary stateV(ρ2 - ρ1)g = f vm (1- ρ1/ ρ2 )g =f v

Advanced Electronic Ceramics I (2004)

Stoke’s equation 1(assumption)1. Laminar flow(small Reynolds number)2. Spherical shape3. 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 byf = 6π η R

Advanced Electronic Ceramics I (2004)

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)

Photo-sedimentation

h

t = 0 t = t1

Narrowhorizontalbeam of parallellight

Photocell

Intensity increases as increasing sedimentation time

R = =9ηv

2(ρ2- ρ1)g9ηh

2(ρ2- ρ1) g t

1/2 1/2

Intensity⇒ particle-size distribution

The use of white light

Advanced Electronic Ceramics I (2004)

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.

Photo-sedimentation: example

http://www.ssi.shimadzu.com/

♦ 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

Why centrifugal?- increase the sedimentation speed of fine particles by several orders of magnitude. - greatly moderates the effect of Brownian motion.

Advanced Electronic Ceramics I (2004)

X-ray sedimentation

The use of X-ray

I=Ioexp(-BC)D=log (I/Io)

I: Resultant X-ray densityIo: Incident X-ray densityB: constantC: concentration of powder in the beamD: X-ray density

Advanced Electronic Ceramics I (2004)

Sedimentation

Possible errors in sedimentation technique1. Hindered settling due to particle interactions2. The tendency of fine particles to be pulled along behind large ones3. Agglomeration caused by Brownian motion

Typical time for the 1 cm sedimentation (alumina in water)1. 1 min for 10 µm alumina2. 2h for 1 µm alumina

Disadvantages1. Requires the densities of materials2. Not good for emulsion where the material does not settle3. Not good for very dense material that settles too quickly4. Need to keep constant temperature for constant viscosity of medium

Advanced Electronic Ceramics I (2004)

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)

Laser diffraction

d > 50 µmFraunhofer approximationdiffraction of light outside of the crosssection of the beam

d < 50 µmMie approximationtakes into account both diffraction 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 fromhttp://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)

Laser diffraction: example

http://www.ssi.shimadzu.com/products/5_test_and_physical_measurement/sald2001.html

Advanced Electronic Ceramics I (2004)

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.

Photon Correlation Spectroscopy(Light Intensity Fluctuation)

Www.photocor.com

Advanced Electronic Ceramics I (2004)Www.photocor.com

Photon Correlation Spectroscopy: example

Measurement rangeParticle size: 1 ... 5000 nm Diffusion coefficient 10-5 ... 10-10 cm2/s Molecular weight 102 ... 1012 g/mol