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Aem Lect5 Aem Lect5 Presentation Transcript

  • 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 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)
  • 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)
  • 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)
  • 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)
  • 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 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)
  • 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)
  • 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 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)
  • 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)
  • Photon Correlation Spectroscopy: example Measurement range Particle size: 1 ... 5000 nm Diffusion coefficient 10-5 ... 10-10 cm2/s Molecular weight 102 ... 1012 g/mol Www.photocor.com Advanced Electronic Ceramics I (2004)