Aspek Fisika dari Struktur Partikel

Powder characteristics

Single particle characteristics Particle systems

Primary chemical composition Distribution of chemical compostionImpurity composition and distribution Distribution of impuritiesPhase composition (Mineralogy) Distribution of phase compositionsCrystal defects Porosity and pore structurePorosity, pore structure Particle size distributionSize Particle shape distributionShape Bulk densityDensity Specific surface areaSpecific surface area Bulk composition

Agglomeration state

The underlined properties are routinely determined

Definition of diameters:

Equivalent sphere (volume) diameter

Minimum, maximum diameters

Sieve diameter (minimum mesh size through which the particle will fall)

Aspect ratio: longest diameter/shortest

Particle size

Chord length in particularreference direction

Frequently used particle sizes

1.The Stokes diameter is the diameter of a spherical particle that has the same density and settling velocity as the particle (laminar flow)

2.The aerodynamic diameter is the diameter of the water droplet that has the same settling velocity in air.

3.The volume diameter is the diameter of a sphere having the same volume as the particle.

4.The surface-volume diameter is the diameter of a sphere having the same surface-to-volume ratio as the particle.

5.The sieve diameter is the width of the minimum square aperture through which the particle will pass.

6.The Feret's diameter is the mean value of the distance between parallel lines tangent to the outline of the particle.

Laser Laserlight

Detector

When a light beam illuminates an aerosol, some light is transmitted through a suspension, while some is absorbed and some is scattered by the particles. The light scattered by a particle is a function of its size, shape, refractive index and the wavelength of the incident beam. For particles with refractive index nP , wiith a diameter R smaller than the wavelength of the laser light and suspended in a medium with refractive index nM, (n= nP / nM) the intensity Is scattered at angle can be described by the equation given by Raleigh:

Is()I0

1

r216 4

2R6

4n2 1n2 2

2

1 cos2

For particles larger than the wavelenght of light the Raleigh equation does not hold anymore and the Mie scattering theory has to be applied. Each particle gives a Fraunhofer diffraction pattern which overlap.

Suspension

Particle size measurements: Light diffraction I

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are needed to see this picture.

- 0 +

Intensity

- 0 +

Particle size measurements: Light diffraction II

Powder characterisation

Scattered intensity as function of scattering angle for three individual particles (red < blue < green)

Sum of the scattered intensities shown on the left.

Fraunhofer diffraction pattern (2.5x) of a particle of unknown size. The position of the center of the dark areas is related to particle size a by the following equation

Fraunhofer diffraction aureole around the sun caused from arctic haze aerosol

Particle size measurements: Light diffraction III

Particle size distributions I

Representation of particle size distributions

(Reed, 1995)

size (mm)

monodispersed

polydispersed

1 105 100

100%

50%

10%

Type of particle size distributions

Mean particle size

Definition of different arithmetic and geometric mean particle diameters (mathematical function of the size distribution function unknown):

dL Ni diNi

On a number of particle basis:

Ni = Number of particles in class idi = mean diameter of particles in class i

lnd Ni lndiNi

Arithmetic mean

Geometric mean

If the fractional size distribution is given on a mass basis, the following equation allows to convert it to a number basis distribution:

Ni M i

Vdi3

Ni = Number of particles in class iMi = Mass of the particles in class i = density of particlesv = volume shape factordi = mean diameter of particles in class i

« length diameter »

dS Ni di

2Ni

dV Ni di

3Ni

3

« surface diameter » « volume diameter »

Particle shape

A dimensionless combination of different average diameters of a distribution of particles is called a shape factor. Shape factors have three functions:

-Proportionality factors between different particle size determination methods-Conversion factors for expressing results in terms of an « equivalent sphere » dimension-Transformations of the measured particle diameter into particle surface and volume respectively.

V VtNi di

3Vt = Total volume of the particlesNi = Number of particles in class idi = mean diameter of particles in class i

The volume shape factor is defined as:

The most common shape factor is the aspect ratio e.g. the ratio between the largest and the smallest diameter of a particle.

Well dispersed hard or soft agglomerated

Agglomerated powders should be dispersed by ultrasonic treatment or milling before use.

Agglomeration state:

Agglomeration states I

Hard agglomerates in alumina produced by the Bayer-process.

As recieved zirconia powderwith soft agglomerates.

Zirconia powder shown in thecenter image after dispersion.

(Reed, 1995)

Particle density I

Density

open porosity(Vop )

closed porosity (Vcp )

Densities:ultimate density: M/Vs

apparent density: M/(Vs + Vcp)bulk density: M/(Vs + Vcp + Vop)

M: particle mass (empty pores)Vs : volume of solid

PycnometryThis method allows to measure the apparent density.

(Reed, 1995)

The mercury injection porosimeter allows to measure the open porosity

The volume of mercury (contact angle with most solids = 140°) forced into the pores of the solid is mesured as a function of pressure. The pore size distribution is calculated using the relationship between applied pressure and the radius of the pore which can be filled by this pressure

= wetting angle (140° for most solids)

= surface tension mercury - sample

r = pore radius

p2 cosr

(Reed, 1995)

Particle density II

Powder characterisation

Cumulative pore volume curve as function of pore size. Hysteresis is usually obeserved. This reflects some of the mercury being permanently trapped in « ink bottle pores ». The volume of the latter is given by the residual Hg entrapped when Hg pressure is reduced to atmospheric presssure.

Particle density III

Three ink-bottle pores

Cumulative pore volumes for alumina powder containing agglomerate of a) porous particles b) non-porous particles.

a

b

Specific surface area

Specific surfaces are determined by measuring the amount of nitrogen gas adsorbed at the surface (BET method) Assumption: only one layer of nitrogen is adsorbed. The specific surface is given by

The solid must be free from previously adsorbed gases and vapours. Evacuation at 10-4 Torr for several hours is necessary. It is possible to heat the solid (100-400°c).

S NAVM AMVMolM s

NA: Avogadro’s number VM: adsorbed gas volumeAM: area occupied by one adsorbate moleculeVMol:volume of one mol of gas at standard P,TMs: mass of the sample

Measuring setup for BET (Bernauer, Emmet and Teller) measurements.

Powder specifications I

Specifications for three Bayer process aluminas

Powder characterisation

Powder specifications II

Specifications for three barium titanate powders

Progress of segregation (a-c) that results after bidisperse color-coded particles are poured into a silo. A sharp reduction of segregation is observed when a small volume fraction of fluid is added which introduces capillary bridges between particles (d). http://physics.clarku.edu/~akudrolli/wet-seg.html

Powder segregation I

Powder segregation II

Simulation of particle size segregation during vibration. Interestingly the large particles move upward = Brazilian nut effect! (http://www.granular.com/POWDER/tour.html)

The Langmuir isotherm can be tested in arranging it in a linear form:

can hardly be determined, but the volume v of gas taken up by the sample can be measured. The ratio between the volume of the adsorbed gas (v) and the maximum volume uptake (V) assumed to correspond to a total monolayer coverage is proportional to the surface coverage.

so A plot of P / v against P is linear.

The intercept allows to determine K at constant T.

KPa KPa

KPa

KPa

KPa 1

Langmuir isotherm II

vV

Pav

PaV

1KV

Microcrystalline cellulose is one of the most useful filler for direct compression. Cellulose in general consists of an amorphous part and a crystalline part, which can exist in two polymorphic forms: cellulose I and cellulose II. UICEL (University of Iowa cellulose)

is a cellulose II product and can be obtained by mercerization (chemical treatment with sodium hydroxide) from Avicel PH102®, a microcrystalline cellulose, which contains the cellulose I polymorph. X-ray measurements of the two substances confirmed the different polymorphic forms and demonstrated a higher degree of crystallinity for Avicel PH102®(73%) than for UICEL (64%).

Cellulose exists in four major crystal modifications, cellulose I, II, III and IV. The polymorphic forms can be interconverted according to figure 3 mostly by certain chemical and thermal treatments

Figure 3: Interconversion of the polymorphs of cellulose.

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