particle characterization

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L U N D U N I V E R S I T Y

Particle characterization

Chapter 6

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L U N D U N I V E R S I T Y

Why determinate particle size

• List three things that you know will be affected by particle size

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L U N D U N I V E R S I T Y

My three things

• Delivery of particles to the lungs• Solubility of active pharmaceutical

compounds• Bulk density

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L U N D U N I V E R S I T Y

What do you want to characterize

Particle• Size • Morphology• Material properties

– Porosity– Density– Hardness/

elasticity(later)• Surface properties

– Chemical composition– Surface energy– Roughness

Powder• Particle distribution• Flowability/cohesion• Specific surface• Density• Porosity• Air content• Water content (later)

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L U N D U N I V E R S I T Y

Size and Morphology Describe these two particle collections

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L U N D U N I V E R S I T Y

Size and Morphology Different descriptive terms for particles

Particle formspherical, ellipsoid, granular, blocky, flaky, platy,prismodal, rodlike, acicular, needle shaped, fibrous irregular,dendrites, irregular, agglomerates

But also particle surface Smooth, spotty, rough, porous, with cracks, hairy

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L U N D U N I V E R S I T Y

Size and Morphology Measurement of particle size

• Reduce to known geometry– Volume

• Cubes• Spheres• Ellipsoids

– Area• Circles• Squares• Ellipses

– Lengths• Characteristic lengths• Feret and Martin

diameters• Relate to the geometry

– Fit into the geometry– Have equal Volume or Area– Have equal properties

A= Projected a reaP=Perimeterd=equivalent diameter S=surface areaV=volume

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L U N D U N I V E R S I T YSize and Morphology Descriptors based on diameters of circles

dcirc=Diameter of circumscribed minimum circledinsc=Diameter of inscribes maximum circledeq=Diameter of the circle having same area as projection area of particle

Shape descriptor:Circularitydeq/dcirc

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L U N D U N I V E R S I T YSize and Morphology More descriptors according to the same principles

Namn Definition Formula

Volume diameter

Diameter of a sphere having the same volume as the particle

Surface diameter

Diameter of a sphere having the same surface as the particle

Surface volume diameter

Diameter of a sphere having the same surface to volume ratio as the particle

Projected area diameter

Diameter of the circle having the same area as the projection area of particle

Perimeter diameter

Diameter of the circle having the same perimeter as the projection peramiter of particle

€

V = πd3

6

€

S = πd2

€

dsv = dv3 /6d

s

2

€

A = πd2

4

€

P = πd

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L U N D U N I V E R S I T Y

Size and Morphology Feret and Martin diameter

• The Feret diameter the distance between two tangents to the contour of the particle in a well defined orientation.

• The Martin diameter, is the length of a line that divide the area of the particle into two equal halves.

• Normally measured– Mean= the mean over

several orientations– Y=largest– X=smallest– Elongation= Y/X

Df0

Dm0

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L U N D U N I V E R S I T Y

Size and Morphology Unrolled diameter

• The mean chord length through the center of gravity of the particle

€

E(dg) =1

πdg

0

2π

∫ dθg

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L U N D U N I V E R S I T Y

Size and Morphology Diameter Defined from equal properties

Drag diameter• Diameter of a sphere having the same resistance to motion

as the particle in a fluid of the same viscosity and the same speed

Free-falling diameter• Diameter of a sphere having the same density and the same

free-falling speed as the particle in a fluid of the same density and viscosity

Stoke diameter• The free falling diameter of a particle in the laminar flow

regionAerodynamic diameter• the diameter of a sphere of unit density (1g/cc) that has the same

gravitational settling velocity as the particle in question.

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L U N D U N I V E R S I T Y

Size and Morphology Stoke diameter

• For small particles <0.5m Brownian motions counteract gravitational forces and the system will be stable

• For larger particles

• Density matching will hinder sedimentationmpart*g

msolvent*gBrownian motion

v=2a2gΔρ

9η

D=kT

6πηaa

€

v =2d2gΔρ

18μ

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L U N D U N I V E R S I T YSize and Morphology Diameter Defined from equal properties contin..

Equivalent light-scattering diameter• Diameter of the sphere giving the same intensity

of light scattering as that of a particle, obtained by the light-scattering method

Sieve diameter• The diameter of the smallest grid in a sieve that

the particle will passe through

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L U N D U N I V E R S I T Y

Size and MorphologyFrom descriptors

• Elongation: L/B or dferet(max)/dferet (min)

• Circularity: for example dins/dcirc• Sphericity (Wandells):

€

Ψ=πdv

2

Sp

=dv

ds

⎛

⎝ ⎜

⎞

⎠ ⎟

2

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L U N D U N I V E R S I T Y

Size and Morphology Form descriptors

• Form factors: f/k will describe the form

• Space Filling Factor: The ratio between the area of a circumscribed rectangle or circumscribed circle of the image and that of the particle eg A/LB eller 4A/πr2

€

Sp = f * da2

Vp = k * da3

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L U N D U N I V E R S I T Y

Material propertiesDensity

• True particle density: The density of the material

• Apparent particle density: Density of the particle when inner porosity is included

• Effective or aerodynamic particle density: Density if outer porosity is included. Related to the density that a air or gas stream will measure.

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L U N D U N I V E R S I T Y

Surface properties Particle surface

• Properties– Roughness of the surface– Composition– Surface energy

• Influences– Stability– Total area– Particle size reduction– Adsorption of other

substances to the surface– Aggregation– Release of adsorbed

material

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L U N D U N I V E R S I T Y

Surface properties To evaluate surfaces properties

• ESCA, XPS - Composition

• FTIR - Composition• AFM- Surface

morphology and surface energy

• Raman microscopy- composition

• Electron microscopy -Surface morphology

Evaluation of Ascorbyl Palmitate-loaded NLC Gel using Atomic Force MicroscopyV.Teeranachaideekul.1,2, S. Petchsirivej3,4 , R.H. Müller1, V.B. Junyaprasert2

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L U N D U N I V E R S I T YSurface properties To evaluate surface energy - Contact angles

• Gives information on how easily a liquid wets a surface.

• Low contact angle with water for hydrophilic surfaces.

• Contact angle hysteresis:– Chemically

heterogeneous surface.– Surface roughness.– Surface porosity– Surface changes when

wetted.

L/V

S/VS/V

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L U N D U N I V E R S I T Y

Assignments particlesTask

• Test and compare two different techniques for size determinations (half a day)– Microscopy– Light scattering

• Answer the questions in the assignment description on a seminar (Tue 28 Apr 13.15)

• As usuell hand in a short technical note

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L U N D U N I V E R S I T Y

Assignments particlesPractical issues

• Do the assignment in groups of three• Use our sample or your own• Microscopy use the microscope to take

picture but do the major part of the analyses afterwards Image J is a free program

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L U N D U N I V E R S I T Y

Size distribution Particle size distribution

• Why is the mean value not enough to describe particle size distributions

• How can we describe the distribution– Based on what properties– Based on what type of statistic distribution

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L U N D U N I V E R S I T Y

Size distribution Type of distributions

• Different type of diameters

• Different type of distribution– Number (0)– Length (1)– Area (2)– Volume (3)– Weight (w) =V*

• How will these differ from one another?

• How do you calculate the mean particle size

• Can you transfer mean particle size between the different distributions?

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L U N D U N I V E R S I T Y

Size distributionAverage particle size

Number mean length diameter d(1,0) 2

Number mean surface diameter d(2,0)

2,16

Number mean volume diameter d(3,0)

2,29

Weighted mean length diameter d(3,0)

Length surface mean diameter d(2,1)

2,33

Length volume mean diameter d(3,1)

2,45

Surface Volume mean diameter d(3,2) 2,57

weight moment mean diameter d(4,3)

2,72

€

d = dS∑ dN∑

€

d = dL∑ dN∑

€

d =3

dV∑ dN∑

€

d = dL∑ dw∑

€

d = dS∑ dL∑

€

d = dV∑ dL∑

€

d = dV∑ dS∑

€

d = dM∑ dW∑

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L U N D U N I V E R S I T Y

Size distributionDifferent distributions

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

1 2 3

size

distribution

N

L

S

V

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L U N D U N I V E R S I T Y

Size distribution Type of statistic distribution

Normal distribution

Log Normal

Rosin–Rammler (Weibull) Distribution

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q = expd

d

⎡ ⎣ ⎢

⎤ ⎦ ⎥

n

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L U N D U N I V E R S I T Y

Size distribution Special properties of log distributions

• If the number is log distributed so is the length, surface, and volume

• With the same geometric mean deviation• Hatch-Choate relationships will transfer

one type of mean diameter into another

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L U N D U N I V E R S I T Y

Size distribution Description of particle size distribution

• Mean diameter– Standard mean, – Geometric mean

• variability– Standard deviation – Geometric standard

deviation• Skewness

€

IQCS =(D75% − Dg ) − (Dg − D25%)

(D75% − Dg ) + (Dg − D25%)=

1

n(xi - x )3∑

1

n(xi - x )2∑

⎛

⎝ ⎜

⎞

⎠ ⎟3 / 2

0 5 10 15 20 25 30 35 40

€

lnd g = dN * ln x∑ N∑

€

lnσ g = dN(ln x − ln x )2 / N∑∑[ ]

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L U N D U N I V E R S I T Y

PowderSpecific surface

• Surface per weight• Factors that increase surface

area– Decrease in particle size– Increase in surface

roughness– Inner porosity (if

available)• Method dependent

parameter– Permeatry– Gas adsorption– Gas diffusion– Porosimetery

• Importance– Dissolution– Chemical reactions– Adsorption of other

molecules– Flow though particle

beds

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L U N D U N I V E R S I T Y

PowderDensity, air content and porosity

• Density (b)= weight of powder/Volume of powder

• Air content= air in pores(entrapped air) and air in between particles (void air)

• Porosity• In particle• Between particles

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L U N D U N I V E R S I T Y

PowderFlow properties and powder density

• Angle of repose

• Bulk density– Tapping density

– Carrs index

– Hausner ration

Flow character

Angle Carrs index

Very good <20 5-15Good 20-30 12-16Ok 18-21Poor 30-34 25-35Very poor 33-38Extremely poor

>40 >40€

Carrsin xdes =tapped − poured density

tapped density

€

Hausner ratio=tapped density

poured density