Powder characteristics Powder characterisation Single particle characteristicsParticle systems...

Powder characteristics

Powder characterisation

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.


after http://hawaii.uvt.tu-clausthal.de/papers/english/rs_1.pdf

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(θ)

I0

=1

r2

16π 4

2⋅

R6

λ4

n2 −1

n2 + 2

⎛

⎝ ⎜

⎞

⎠ ⎟

2

1+ cos2 θ( ) ⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

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. Deconvolution of the total intensity distribution allows to extract particle size distribution. Dynamic scattering measurements, which use the Doppler shift of the diffracted light due to the movement of the particles, allow to cover a much larger diameter range. Laser scattering techniques can cover a tremendous range of particle sizes from nanometers up to 2000m.

Suspension

Particle size measurements: Light diffraction I


QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

- 0 +

Intensity

- 0 +

Particle size measurements: Light diffraction II


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

What is the shape of the particle? Calculate the diameter in x and y direction for a wavelength = 633 nm and a distance of the screen from the particle = 7.3 m.

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


Difference between two particle size measurement methods.

(Reed, 1995)

Particle size distributions II


Mean particle size

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

dL =Ni ⋅di∑

Ni∑

On a number of particle basis:

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

lnd =Ni ⋅lndi∑

Ni∑

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

ρψVdi3

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

« length diameter »

dS =Ni ⋅di

2∑Ni∑

dV =Ni ⋅di

3∑Ni∑

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.

ψ V =Vt

Ni ⋅di3∑

Vt = 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.

For a population of spheres, ψV is /6, for spheroids and cylinders taking the minor axis and the diameter respectively as D, the volume shape factor increases with increasing length L to width ratio f.ex. for cylinders:

L/D ψV 0.5 3.14

1 4.712 7.854 14.14


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)


Aggregation of particles in a sheared 2d fluid. Simple stirring of a suspension is not a good method to disagglomerate a powder [S. Schwarzer, http://www.ica1.uni-stuttgart.de/Movies/].

Agglomeration states II


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

Δp=2γcosθ

r

(Reed, 1995)

Particle density II


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 AM

VMolMs

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 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)


Adsorption isotherms Adsorption isotherm: The relationship at a given temperature between the equilibrium amount of gas adsorbed and the pressure of the gas.

Adsorption isotherm for ammonia on charcoal.


Isotherm types

Three phenomena are inolved in adsorption isotherms:

- Monolayer adsorption (Langmuir isotherm).

- Multilayer adsorption (BET isotherm).

- Condensation in pores or capillaries (adsorption hysteresis).

Type I: Langmuir type isotherms. The adsorbed molecules form a monolayer.

Type II: Multilayer physical adsorption on non-porous (microporous) solids.

Type IV: Condensation on porous solid. The usual pore diameter is between 2nm and 20nm. The upper limit of adsorption is governed by the total pore volume.

Type III & V: The initial uptake of gas is slow. Such isotherms (rarely observed) occur when the forces between the first monolayer and the surface are small..

Stepwise isotherms: Each step corresponds to the formation of a complete molecular adsorbed layer.


Langmuir isotherm I

The rate of adsorption of a gas on a surface is given by (monolayer absorbption):

Ka = const. , Pa = Pressure, N: Number of adsorption sites, =fraction of occupied sites

The rate of desorption is proportional to the amount of gas adsorbed:At equilibrium:

with Ka / Kd = K (gas affinity for solid)

at equilibrium

1θ

−1=Kd N

Ka Pa N

dNdt

=KaPaN 1−θ( )

−dNdt

=KdNθ

KaPaN 1−θ( ) =KaNθ

θ=KPa

1+KPa


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.

θ+θKPa =KPa

θKPa

+θ=KPa

KPa = θ1−θ


Langmuir isotherm II

€

=vV⇒ Pa

v= Pa

V+ 1

KV

BET isotherm

Because of the Van der Waals forces physical adsorption is not limited to a monolayer. A molecule may be adsorbed on a bare spot or on top of an already adsorbed molecule resulting in an adsorbed layer consisting of several molecularlayers. BET is an extension of the Langmuir treatment for multilayer adsorption on non-porous materials. The curves rise indefinitely as the pressure is increased because there is no limit of the amount of material which can be adsorbed.

€

Vtot

Vmono

= c p

p0

⎛

⎝ ⎜

⎞

⎠ ⎟ 1−

p

p0

⎛

⎝ ⎜

⎞

⎠ ⎟ 1− (1− c)

p

p0

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

−1

p: Vapour pressure.

p0: Vapour pressure at condensation.

c: Constant.


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