Particle Sizing by Laser Diffraction

$Page 1: Particle Sizing by Laser Diffraction$
© 2017 Malvern Instruments Limited

Particle Sizing by Laser DiffractionDr Anne Virden

Product technical specialist – diffraction and analytical imaging

[email protected]


Overview

› Introduction to particle sizing

› Introduction to laser diffraction

› Smarter particle sizing Smarter method development

Data quality advice

› Method development Method development for dispersion in liquid

Method development for dispersion in air

› Choosing the right specifications Understanding the size distribution

› Optical properties and optical modes


Introduction to particle characterisation

› What is a particle?

› A particle can be defined as:

› ‘a minute portion, piece, fragment, or amount of matter’

› Naturally occurring examples include: Sand, soil, clay, pollen, dust, smoke, fog


Introduction to particle characterisation

› What is a particle?

› A particle can be defined as:

› ‘a minute portion, piece, fragment, or amount of matter’

› The particles that we measure are in:

Dry powders Suspensions Emulsions Sprays


What can measuring particle size tell us?

› Predicting product performance Dissolution rate

Content uniformity

Mouth feel assessment

Stability

Viscosity (of a suspension)

Colour

Flowability (of a powder)


Why is particle size important?

› Controlling production processes Blending

Milling

Dispersion

Tableting


Particles come in many different shapes

(as well as sizes)

How do we describe the size of these particles?


Basic concepts of particle sizing

› You are given a regular-shaped object and a ruler and asked

to give a one-number indication of its size What would your reply be ?


Basic concepts of particle sizing

› You may reply: “360x140x120mm” Which might be correct but it is not one number.

It is not possible to describe the size of this 3-dimensional object with a single

number


Concept of equivalent spherical diameters

› The rectangular box has the same volume as a sphere of

226µm diameter. The volume equivalent spherical diameter is 226μm

226μm


How do we describe the size of a particle?

› Equivalent spheres Maximum length

Minimum length Max. length

Min. length

Max. lengthMin. length




Minimum length

Sedimentation rate

Max. lengthMin. length

Sedimentation rate

Sedimentation rate




Minimum length

Sedimentation rate

Sieve aperture

Max. length

Min. lengthSedimentation rate

Sieve aperture

Sieve aperture




Minimum length

Sedimentation rate

Sieve aperture

Surface area

Max. length

Min. lengthSedimentation rate Sieve aperture

Surface area

Surface area




Minimum length

Sedimentation rate

Sieve aperture

Surface area

Volume

Max. length

Min. lengthSedimentation rate Sieve aperture

Surface area

Volume


Concept of equivalent spherical diameters

› Different particle sizing techniques report different

equivalent spherical diameters Dependent on the physical property that is measured


Introduction to laser diffraction


The basic principles of laser diffraction

› The diffraction pattern:


Dependence of diffraction pattern on particle size

Large particle Small particles

Incident lightSmall angle scattering

Incident light Large angle

scattering


Measuring the scattering pattern: Spraytec

Light source

Measurement zone

Data collection lens Detector system

Collimating

opticsAuto-align stage

Data acquisition

system

IP65 enclosures


Measurement cell Focal plane

detectors

Side scatter

detectors

Back scatter

detectors

633nm red

laser

Precision

folded optics

Measuring the scattering data: Mastersizer 3000


Measuring the scattering data: Mastersizer 3000

470nm blue

light source

Side scatter

detectors

Measurement cell

Back scatter

detectors


The measured scattering data

Increasing angle / Decreasing particle size

Red light detectorsBlue light

detectors

Extinction detectors:

51 and 63


Example data set: large particles

› Large particles scatter at low angles

› Scattering data is concentrated on low angle detectors With high intensity (light energy)


Example data set: small particles

› Small particles scatter light at high angles

› Scattering data is concentrated on high number detectors With low intensity (light energy)


Laser diffraction instrumentation

› Wide dynamic range ideal for polydisperse samples

› Wet, dry or spray measurements

› Ensemble method, good sampling

› Lab (Mastersizer, Spraytec) and process (Insitec) solutions

› Widely accepted and standardized


Particle size measurement ranges

Particle size

Laser diffraction

0.1nm 1nm 10nm 100nm 1μm 10μm 100μm 1mm 10mm

Dynamic light scattering

Sedimentation

Electrozone sensing

Sieving

Nanoparticle tracking

Taylor dispersion analysis

Automated imaging

Spatial filter velocimetry

Resonant mass measurement


Smarter particle sizing


Introducing the Mastersizer 3000

› Extensive measurement capabilities 10nm to 3.5mm range

10kHz data acquisition

› Rapid and effective wet dispersion Efficient in-line sonication

› Cutting-edge dry dispersion Suitable for fragile and cohesive samples

› Software that eases your workload Direct measurement feedback

Method development guidance

Data quality assessment

Easy result reporting


Laser diffraction measurement process

Sampling

Dispersion and stabilisation

Optical alignment

Background signal collection

Sample signal collection

Data analysis

Reporting and interpreting results


When do sampling and dispersion matter?

Particle size

% E

rro

r

Instrumentation

Sampling

Dispersion

Sampling


How much sample do I need to measure

› A certain number of particles must be measured in order to

obtain a representative result For larger particles a greater mass of sample must be measured to ensure sufficient

particles are measured

0.00

0.50

1.00

1.50

2.00

2.50

0 200 400 600 800 1000

Min

imu

m m

ass

/ g

Dv90 / μm

Sampling


Data Quality: Ensure representative sampling

Sampling


The Mastersizer 3000: Wet dispersion units

Hydro EV Hydro LV Hydro MV Hydro SM Hydro SV

Volume/mL 1000/600ml 600ml 120ml 50-120 6-7ml



How do we disperse particles in liquid?

› Stirring and ultrasound are used to disperse agglomerates

1: Before ultrasound 2: During ultrasound 3: After ultrasound



Direct feedback on measurement stability is provided


after ultrasound


Smarter method development: SOP player



Diagnosing stability problems



Hydro Sight

› In-line imaging accessory allowing

users to view the dispersion

› Helps users to optimise and

troubleshoot their methods


Hydro Sight

› Size range Measurement: 9 - 1000 µm

Observation: 1.4 - 1400 µm

› Measures size and elongation Also calculates the degree of sample dispersion

› Works with recirculating liquid

sample dispersion units: Hydro SM / EV / LV / MV

› Simple installation Connected between the dispersion unit and the

optical bench


Hydro Sight aids method development by providing sample

images which show the state of dispersion


Following dispersion trends using Hydro Sight


The software can also be configured to automatically

detect sample anomalies


Dry powder dispersion - Aero

› 0.1 mm to 3500 mm

› Precise pressure control 0.1 to 4.0 bar range

› Modular venturi disperser Standard suitable for most powders

Options for cohesive or abrasive samples

› Modular sample tray design Hopper unit for large sample quantities

Micro and Macro trays for smaller quantities

› Full software control


Exchangeable dispersers enable the development

of a range of applications


Standard Venturi High-Energy Venturi


Data Quality: Optical alignmentOptical alignment


Data Quality: Background

› Background level and stability can be assessed before sample

addition Ensures confidence in measurement quality

Background signal collection


Data Quality: How much sample should I add



Data Quality: How much sample should I add



Data Quality: Optical models and optical properties

› The data quality system provides advice on the choice of

optical model and optical properties

Data analysis


Customise reports for your application

› Customise reports with Graphs

Tables

Parameters

Calculations (text, tables and graphs)

Signature tables

Pictures



Easily review results from multiple record files



Direct support is provided via the Malvern Portal



Choosing the right specificationsThe particle size distribution explained


Understanding particle size results: Distribution type

› Type of distribution result depends on measurement

technique Number

Mass

Volume

Intensity

› Always set specifications using the type of result measured

by the system Transforming the result type greatly increases the potential error


Particle size distribution statistics: Median and Mode

› Median = midpoint of the distribution

› Mode = most commonly occurring size class

Diameter

% V

olu

me

Gaussian Distribution

ModeMedian

%


PSD Statistics: Median and Mode

› If the distribution shape is more complex then these

parameters will diverge

Diameter

% V

olu

me

Mode

Median

49% 51%

Bimodal Distribution

%


PSD Statistics: Percentiles

› Percentiles are the size below which there is a certain

volume of the sample Taken from the cumulative distribution

Diameter

% V

olu

me

Diameter

% V

olu

me

Cu

mm

ula

tive

dis

trib

uti

on

/ %

0

10

20

30

40

50

60

70

80

90

100

Dx10 Dx50 Dx90


PSD Statistics: Mean particle sizes

› The most familiar mean is the arithmetic mean

𝑋𝑛𝑙 = 𝐷 1,0 =11 + 21 + 31

10 + 20 + 30=1 + 2 + 3

3= 2

› Different particle sizing techniques report different mean

sizes, depending on the sensitivity of the technique Image analysis reports a number weighted mean

• D[1,0]

Laser diffraction reports the volume weighted mean

• D[4,3]

• And surface area weighted mean, D[3,2]


PSD Statistics: Volume weighted mean

› D[4,3] is sensitive to changes in the coarse particle fraction Useful for monitoring milling or dispersion

D[4,3] = 11.2

D[4,3] =7.95


PSD Statistics: Surface area weighted mean

› D[3,2] is sensitive to changes in the fine particle fraction Useful when surface area is important

D[3,2] = 34.4μmD[3,2] = 59.1


Diameter

% V

olu

me

Particle size distribution statistics: Summary

› Percentiles

› Averages, weighted by number, surface area or volume

› Avoid parameters with high variability, such as Dx100

Dx10 Dx50 Dx90D[3,2] D[4,3]

Dx100%

D[1,0]


Choosing the right parameter to follow the process

› Blend of coarse and fine particles

0

10

20

30

40

50

60

70

80

90

100

0.1 1 10 100 1000 10000

Cu

mu

lati

ve v

olu

me %

Size / um

coarse

1% fines

5% fines

10% fines

20% fines

30% fines

fines


Choosing the right parameter to follow the process

› Choose the parameter that shows the greatest sensitivity in

the region of interest

0

50

100

150

200

250

300

0 20 40 60 80 100

Siz

e /

um

Fines /%

Dv10

D[3,2]

Dv50

D[4,3]

Dv90


Example: Factors affecting the tableting process

› Particle size Smaller particle size increases particle adhesion

Greater adhesion can lead to voiding, cracking and breakage

Affects flowability of powder into the die

› Particle size distribution Close overlap between actives, excipients and binders is ideal

Narrow distributions improve content uniformity

Wider distributions increase packing density


Example: Tablet formulation



Evolutions in Direct Compression, Douglas McCormick, Pharmaceutical Technology, April 2005. Pg 52-62

Parameter Target value

(μm)

Size specification

(μm)

Dv10 >30 40 ± 20%

Manufacturing spec 32 to 48

D[4,3] >80 110 ± 20%


Dv90 <1000 200 ± 20%



What precision values are reasonable?

› ISO13320-1: Section 6.4 Dv50 - 5 different readings: COV < 3%

Dv10 and Dv90: COV < 5%

“Below 10μm, these maximum values should be doubled.”

› In ideal conditions 0.5% COV on parameters >1μm

1% COV on parameters <1μm

› USP <429> and EP 2.9.31 Provides reproducibility ranges

Dv50 or any central value: <10%

Dv10, Dv90 or any non-central value: <15%




› Specifications should be tightened to account for analytical

variation Ensures that the manufactured material is in specification

› Using the USP guidance for reproducibility 10% on central values

15% at distribution edgesParameter Target value (μm) Size specification (μm)

Dv10 >30 40 ± 20%


(narrow specification by 15%) Measurement limits 36.8 to 40.8

D[4,3] >80 110 ± 20%


(narrow specification by 10%) Measurement limits 96.8 to 118.8

Dv90 <1000 200 ± 20%


(narrow specification by 15%) Measurement limits 184 to 204


Linking measurement data and manufacturing

specifications

How to Establish Manufacturing Specifications, Donald J. Wheeler, Statistical Process Controls Inc.

Posted on spcpress.com May 2003

Particle Size

Product Specification

Measurement Specification

Upper Product

Acceptance Limit

Lower Product

Acceptance Limit

Lower Measurement Limit Upper Measurement

Limit

ss


Method development for dispersion in liquids


The purpose of method development

› A laser diffraction measurement requires

‘a representative sample, dispersed at an adequate concentration in a suitable liquid

or gas’

<USP429>

› Method development must define appropriate Sampling

Dispersion

Measurement conditions


Is sampling or dispersion more important?

› The greatest source of error in particle size measurements

depends on particle size Dispersion is most important for fine particles

Sampling is most important for coarse particles

Choice of dispersant

Sonication

(dispersion energy)

Sampling

Sampling

Measurement time

Dispersant

Fine particlesCoarse particles


What happens to particles during transportation

› Particle can segregate during transit This can lead to sampling bias

Courtesy of A.J. Morris, M. Glover and M. Probert


What happens to particles during transportation

› Particle can segregate during transit This can lead to sampling bias

Courtesy of A.J. Morris, M. Glover and M. Probert

http://www.cmt.york.ac.uk/~ajm143/001run14.mpg


Measuring in the appropriate state of dispersion

Agglomerated Dispersed


The liquid dispersion process

Wetting the sample

Choose an appropriate dispersant

Carry out a beaker test

Use surfactant to improve the dispersion

Adding energy to improve dispersion

Stirring/pumping by the dispersion unit

Application of ultrasound

Stabilising the dispersion

Check repeatability after ultrasound

Additives can be used to prevent re-agglomeration


Wetting the sample

Dispersant

Water/DI water

Organic acids

Alcohols(methanol / ethanol / isopropyl alcohol)

Simple alkanes(hexane / heptane/ iso-octane / cyclohexane)

Long-chain alkanes and alkenes(dodecane / mineral oils / sunflower oils / palm oil)

Po

larity

Dispersant requirements

Sample wetting

Not dissolve the sample

Bubble free

Suitable viscosity

Transparent to the laser beam

Different refractive index to the sample

Chemically compatible with the instrument



Use surfactants to improve

wetting


Wetting the sample



Use surfactants to improve

wetting

Stabilization Examples

Steric Igepal CA-360, Tween 20/80, Span

20/80

Electrosteric Anionic: SDS (sodium dodecylfulfate),

AOT (sodium-bis-2-

etheylhexylsulfosuccinate)

Cationic: CTAB (cetyltimethlammonium

bromide)

DI water DI water + surfactant



0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

Siz

e /

um

Measurement no.

Dx (10) (μm) Dx (50) (μm) Dx (90) (μm)

Stirring



0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

Siz

e /

um

Measurement no.

Dx (10) (μm) Dx (50) (μm) Dx (90) (μm)

Ultrasound



0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

Siz

e /

um

Measurement no.

Dx (10) (μm) Dx (50) (μm) Dx (90) (μm)

After

Ultrasound


Identifying dispersion: obscuration

› Obscuration increases as agglomerates disperse

0

2

4

6

8

10

12

0 5 10 15 20 25 30

Ob

scu

rati

on

/ %

Measurement no.

Obscuration

Ultrasound on

Ultrasound off


Dispersion trend: scattering data

› During dispersion, as the particles get smaller Scattering on inner detectors decreases

Peak shifts to higher angle detectors

Trend across repeat measurements

Loss of scattering on inner detectors

Reminder: detector number increases with angleScattering from larger particles falls on low angle detectors


Dispersion trend: Particle size distribution

› Overlay the results of an ultrasound titration Should show gradual dispersion

Agglomerates dispersing


Without

ultrasound

With

ultrasound

The dispersion process: Verification



0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

Siz

e /

um

Measurement no.

Dx (10) (μm) Dx (50) (μm) Dx (90) (μm)



0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20

Siz

e /

um

Measurement no.

Dx (10) (μm) Dx (50) (μm) Dx (90) (μm)

Admixtures – increase particle charge

• e.g. Sodium hexametaphosphate,

sodium pyrophosphate, Ammonium

citrate

• pH can also be important• ‘The use of zeta potential measurements for

improving dispersion during particle size

determination’ (MRK373)


How stable should the results be?

› ISO13320-1: Section 6.4

Dv50 - 5 different readings: COV < 3%

Dv10 and Dv90: COV < 5%


› In ideal conditions

0.5% COV on parameters >1μm

1% COV on parameters <1μm


Checking the stability of the results

› The live trend shows the variability of the results RSDs should be within ISO limits

13.3μmAv RSD13.3 0.465%

Av RSD7.32 0.11%

Av RSD3.77 0.0357%

7.32μm

3.77μm


How do measurement conditions affect results?

› Appropriate amount of sample Good signal to noise ratio

Avoid multiple scattering

› Correct stir speed Fast enough to prevent sedimentation for large/dense particles

Slow enough not to break emulsions

› Correct measurement duration Long enough to sample all of the particles in the dispersion unit


What defines the low obscuration limit?

› Signal to noise ratio Large particles scatter a lot of light

Even at low obscuration's there will be a lot of sample data (relative to the

background and noise)Scattering from ~40 micron glass

beads, at 7% obscuration, produces ~250 units of light energy

- significantly higher than the background



› Signal to noise ratio Small particle scatter light more weakly

It is important to make sure that the background is stable before measuring fine

particles

Scattering from 2 micron latex, at 5% obscuration produces ~8 units of light energy – still sufficiently higher than

the background



› The reproducibility of the measurement may also define the

low obscuration limit Particularly if the particle size is large and the distribution is broad

› You can test this by measuring several sub samples of your

material If the results are within acceptable variation then the obscuration is sufficient

Measurements with high variability may be improved by measuring at higher

obscuration (more sample)


What defines the upper obscuration limit?

› If we add too much sample the results may be affected by

multiple scattering This generally affects samples smaller than 10μm

Measurement cell

Dete

cto

r

Low angle

detectors

High

angle

detectors


What defines the upper obscuration limit?

› If we add too much sample the results may be affected by

multiple scattering This generally affects samples smaller than 10μm

Measurement cell

Dete

cto

r

Low angle

detectors

High

angle

detectors

Increase in

scattering angle


How does multiple scattering affect the results

› This can be tested by measuring at increasing obscuration

› For this 1μm sample results at obscurations of 9% and

above show a reduction in size due to multiple scattering

Obscuration (%) Dv (10) (μm)

5.3 0.38

7.04 0.37

9.17 0.34

14.78 0.27

18.81 0.20


Target obscuration ranges: Wet measurements

Particle size range Example Obscuration

Very fineVery low obscurations are used to avoid

multiple scattering

<5%

FineLow obscurations are used to avoid multiple

scattering

5% to 10%

CoarseHigher obscurations are used to improve

sampling

10% to 20%

Very polydisperseHigher obscurations are used to improve

sampling- test with multiple sub samples

10% to 20%


Determine the correct stir speed

› For coarse or dense materials particle size will increase with

stir speed until all particles are suspended A stable particle size is obtained above 2500rpm

0

20

40

60

80

100

120

140

160

180

500 1000 1500 2000 2500 3000 3500

Pa

rtic

le s

ize

/ μ

m

Stir speed / rpm

d10 dv50 d90


Determine the correct measurement duration

› For broad distributions measurement duration must be

sufficient to sample all particles in the system.


Affect of measurement duration on variability

› Result variability is reduced as measurement duration is

increased Variability is within ISO limits when duration ≥10s

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25

% R

SD

(D

v50)

Measurement duration / s


Summary of wet method development

› Dispersion Choice of dispersant

Adding energy to disperse agglomerates


Verifying the state of dispersion

› Measurement conditions Sample concentration – obscuration

Stirrer speed – particle suspension/shearing

Measurement duration


Method development for dry dispersion


When is dispersion important

› The greatest source of error in particle size measurements

depends on particle size Dispersion is most important for fine particles

Sampling is most important for coarse particles

Air pressure

Feed rate

Sampling

Fine particlesCoarse particles

Sampling

Air pressure

Feed rate


Dry powder dispersion: Mechanisms

› Importance of each mechanism depends on: Disperser geometry

Flow rate or air pressure

Material type

› Higher impact energies may improve the dispersion

effectiveness Needs to be balanced against the risk of particle break-up

Energy/aggression


Dry powder dispersion: Disperser design

› Standard disperser Straight through design

No direct wall impaction

Suitable for most types of sample

› High energy disperser Elbow design

Direct impaction surface

Suitable for robust aggregated samples


Ob

scu

rati

on

Time

Ta

rget

ra

ng

e

Step 1: Setting the feed rate

› Keep the obscuration in range during the measurement


Dry powder dispersion: ISO guidance

› Degree of dispersion is controlled by primary air pressure Monitor change in size distribution with pressure

• Carry out pressure titration – Step 2

› Check that particle breakup has not occurred Compare dry results to a well dispersed wet measurement – Step 3

Choose the pressure which agrees with the wet results

• Shows dispersion and not particle breakage

Dry dispersion steps:

Step 1: Set up feed rate

Step 2: Measure pressure titration

Step 3: Compare to reference result


Step 2: Measure a pressure titration

› Make measurements at 4, 3, 2, 1, 0.5 and 0.1 bar.

› Make repeat measurement at each pressure to check for

sample segregation


Step 3: Compare dry results to wet

› Low pressure dry result shows larger result Indicates sample is not fully dispersed


Step 3: Compare dry results to wet

› High pressure shows good agreement Suggests the material is dispersed


Optional Step 4: High energy venturi

› For robust, highly agglomerated materials the high energy

venturi may be required.

Low pressure

High pressure


Comparing standard and high energy venturis

40

50

60

70

80

90

100

110

120

130

140

0 0.5 1 1.5 2 2.5 3 3.5 4

Dv50 /

um

Air Pressure / bar

Aero Standard Aero High Energy Wet Dispersion


Segregation in dry measurements

› Segregation can occur with free-flowing powders with wide

particle size distributions Characterized by a decrease in size over repeat measurements

Make several quick repeat measurements at each pressure

This can be done as part of the pressure titration


Segregation in dry measurements

› Segregation can occur with free-flowing powders with wide

particle size distributions Characterized by a decrease in size over repeat measurements

Make several quick repeat measurements at each pressure

This can be done as part of the pressure titration

› Always measure the whole sample, either by: Making enough short measurements to use the whole sample and then create an

average

Make one long measurement long enough to use up all of the sample.


Summary of dry method development

› Dispersion mechanisms

› Measurements conditions Feed rate

› Pressure titration Comparison to well dispersed wet measurement

› Segregation


Optical properties and optical models


What does laser diffraction measure?

› Laser diffraction systems measure the scattering pattern

produced by an ensemble of particles suspended in a laser

beam


What does an optical model do?

› An optical model predicts the scattering pattern produced by

a particle


What does an optical model do?

› And can predict the scattering pattern produced by many

particles

Size classes / m

0.01 0.1 1 10 100 1000 10000

Vo

lum

e d

en

sity

/ %

0

2

4

6

8

10


How do we use the optical model?

› The Mastersizer measures scattered light energy vs angle

for samples of unknown size distribution

› An optical model can predict the scattering pattern

(scattered light energy vs angle) given a known particle size

distribution

› To obtain a particle size distribution from an unknown

sample we must use the optical model as part of a iterative

process…


Use opticalmodel

How do we use the optical model?


Scattering models: Mie Theory

› Models the interaction of light with matter Assuming that the particles are spherical

Assuming that it is a two phase system

› Valid for all wavelengths of light and all particle sizes

› Predicts the dependence of scattering intensity on particle

size

› Predicts that secondary scattering is observed for small

particles

‘For particles smaller than about 50μm Mie theory offers the best general solution’

ISO13320

http://images.google.com/imgres?imgurl=http://www.physik.uni-halle.de/~tpqhe/old/geschichte/personen/mie/mie.jpg&imgrefurl=http://www.physik.uni-halle.de/~tpqhe/old/geschichte/personen/mie/p_mie.htm&h=749&w=500&sz=57&tbnid=ekWEMc4Qu4kJ:&tbnh=139&tbnw=93&start=5&prev=/images?q=gustav+mie&hl=en&lr=&ie=UTF-8&safe=off&sa=G


Mie Theory: Predicted scattering

Refracted light


Mie Theory: Optical properties

Absorption

“….. the Mie theory offers the best

general solution.”

ISO 13320: 2009


Scattering models: Fraunhofer approximation

› Basic assumption are similar to Mie Theory Assumes the particles are disc shaped

Assumes it is a two phase system

› Plus the additional assumptions that The refractive index difference is high (RRI > 1.3)

The particles are opaque

The wavelength of light is much smaller than the particle size

The angle of the scattered light is small

› In the Mastersizer 3000 software the Fraunhofer approximation is

available as a particle type

‘The advantage of this equation is that it is relatively simple and quick to calculate

‘This Fraunhofer approximation does not make use of any knowledge of the optical

properties of the material’

ISO13320

http://images.google.com/imgres?imgurl=http://academic.brooklyn.cuny.edu/history/virtual/portrait/fraunhofer.jpg&imgrefurl=http://academic.brooklyn.cuny.edu/history/virtual/portrait.htm&h=218&w=183&sz=6&tbnid=a0Tq_JmNJu8J:&tbnh=101&tbnw=85&start=12&prev=/images?q=fraunhofer&hl=en&lr=&ie=UTF-8&safe=off&sa=G


Scattering models: Fraunhofer approximation


Comparing the results of the scattering models

‘If the Fraunhofer approximation is applied for samples containing an

appreciable amount of small, transparent particles, a significantly

larger amount of small particles may be calculated.’

ISO13320

Mie TheoryFraunhofer Approximation


Mie vs Fraunhofer: Data quality advice


Mie vs Fraunhofer: Data Quality advice


Which optical properties do we need?

› To use Mie theory correctly we need to know three optical

properties The refractive index of the dispersant

The refractive index of the sample material

The absorption of the sample material

• Also called the imaginary part of the refractive index

‘Good understanding of the influence of the complex refractive index in the light scattering

from particles is strongly advised in order to apply the Mie theory or the Fraunhofer

approximation appropriately.’

ISO13320


The absorption (or imaginary refractive index)

› The absorption can be determined by looking at the

dispersed sample under a microscope and observing its Shape

Transparency

Internal structure

› Absorption is generally required to a factor of 10 E.g. 0.1 or 0.01 (not 0.023)

Images of some calcium carbonate

particles, an absorption of 0.01 would be

used for these particles, due to the

observed transparency of the particles.


Estimating absorption from particle appearance

0

0.001

0.01

0.1

1.0+

Latices

Emulsions

Slightly colored powders

Crystalline milled powders

Highly colored

(complementary) and metal

powders

Appearance Absorption Example


Methods for determining the refractive index

› Four main routes to refractive index information

References

ISO 13320 appendix

Malvern material database

CRC handbook

Manufacturers label (dispersant)

Online (luxpop, webelements,

google scholar)

Microscope observations

Empirical/semi-empiricalRefractometer measurements


Choosing the refractive index

› A Refractive Index is generally only required to 2 decimal

places e.g. 1.42 not 1.4234

And to an accuracy of ±0.02

› Can be estimated based on similar materialsRefractive index

1 2 31.5 2.5

Plastics and elastomers (1.38 – 1.57)

Inorganic salts (1.52 – 1.8)

Organic compounds (1.4 – 1.7)

Metal Oxides (1.6 – 2.5)


Assessing the data fit

› The fit report shows the measured and calculated scattering

data

› How well these overlay is known as the data fit

› The residual quantifies how good the fit is Residual = area between the two curves

Residual = 0.83%


Inspecting the data fit: refractive index

› A poor fit to the focal plane or side-scatter detectors

suggests an incorrect choice of refractive index

Poor fit indicates incorrect choice of

refractive index


Inspecting the data fit: absorption index

› Misfits to the extinction detectors indicate an incorrect

absorption value 51 in the red light

63 in the blue light

Poor data fit here indicates poor choice of absorption

Poor data fit here indicates poor choice of absorption


Example - weighted

Example - unweighted

Weighted and un-weighted data fits


Assessing the data fit: Example

› The user is seeing an “unexpected” mode of small material.

› The optical properties used were: RI:1.4, Absorption: 0.01


Assessing the fit using 1.4/0.01

Weighted fit Weighted Residual = 3.26

Poor fit = incorrect RI

Un-Weighted fit Residual = 0.82


Assessing the fit using 1.54/0.01

Weighted fit Weighted residual = 0.48

Un-Weighted fit Residual = 0.57 Improved fit


Looking at the results

› Sample is calcium carbonate Reference RI is between 1.53 and 1.63


The optical property optimiser (OPO)

› Offers a quick way to adjust optical properties and assess

the fit and result


Overview

› Introduction to particle sizing

› Introduction to laser diffraction

› Smarter particle sizing Smarter method development

Data quality advice

› Method development Method development for dispersion in liquid

Method development for dispersion in air

› Choosing the right specifications Understanding the size distribution

› Optical properties and optical modes

Date post:	15-Oct-2021
Category:	Documents
Upload:	others
View:	3 times
Download:	0 times

Particle Sizing by Laser Diffraction

Documents