1. Malvern Instruments
Training Course

2. Describing Particle Size
Particles come in
all different
shapes and sizes
The problem is
deciding on the
best way to
describe them

3. Microscopy
A very powerful technique as it allows direct observation of particles within the approximate size range microns.
Produces a number distribution based on measurement of diameters - or more usually projected area diameters.

4. Microscopy - Advantages
Allows direct observation of the particles rather than observing a property dependent on particle size.
The dispersion of the sample can be assessed
Initially easy to set up and use
A good back-up with other methods (e.g. Diffraction and S.O.P’s)

5. Diameters. Feret’s diameter - distance between parallel tangents.
Martin’s diameter - length of bisector.
Longest diameter.
Perimeter diameter - diameter of circle with same perimeter.
Projected area diameter - diameter of circle with same area.

6. Microscopy
Since many particles have to be measured if any degree of confidence is to be achieved automation of the process is required.
Electron microscopy
Sample preparation is elaborate.
Fewer images/particles can be measured per day.
Image Analysis
Quick but software must be good enough to resolve particle boundaries.

7. Microscopy -Disadvantages
Sampling of the distribution is poor! It is impossible to measure all the particles present!
The result is a number distribution not a volume distribution.
Ignoring one 10um particle is the same as ignoring um particles!!

8. Sedimentation A technique used in the paint and ceramics industries.
Requires particles in a fluid to settle under gravity
Limited particle size range since...

9. Sedimentation
Largest particles fall quickly through the medium and can be missed.
Smallest particles are held in suspension for extensive periods

10. Sedimentation - Advantages
A relatively cheap technique to use if you have the time!
Capable of producing reproducible results if used in the right hands.

11. Sedimentation.

12. Sedimentation - Disadvantages
Since Stokes law depends on the viscosity of the fluid, temperature has to be well controlled.
Unable to handle mixtures of different density.
The technique is slow
Tends to underestimate sizes

13. Electrozone Sensing - (Coulter Counter)
Developed in the 1950’s for counting blood cells which are monodisperse suspensions in a weak electrolyte.

14. Electrozone Sensing - (Coulter Counter)
Particles are made to flow through a small orifice in a glass tube which has a voltage across it.
As particles pass through the orifice the voltage changes, this is measured by using a pulse height analyser. The height of the pulse is proportional to the size of the particle.

15. Electrozone Sensing - (Coulter Counter)
Disadvantages
Difficult to measure emulsions
Must measure in Electrolyte
Requires regular calibration
Very poor dynamic size range
Lowest size set by the orifice selected - around 2 microns.
Porous particles give problems

16. Electrozone Sensing - (Coulter Counter)
Summary
Good technique for blood cells but not suitable for most industrial materials
High resolution for narrow distributions,

17. Sieving.

18. Sieving A widely used method of particle sizing.
Woven wire sieves cover size range of 20um to 125mm.
Punched hole sieves available to cm range
Micromesh sieves extend the range down to 5um.

19. In practice particles will look more like this and there will always be some that in volume or weight terms are larger than their equivalent sieve measurements.
Shape must be considered for this technique
Sieving...

20. Sieving - a common question
“ I sieved my material to 110um but laser diffraction tells me I still have particles larger than 110um. How can this be so?
Imagine we have a sieve of 110um hole construction…...

21. Sieving 100um 100um Volume of cube = 106 um3.
Diameter of sphere with the same volume as cube =124um

22. Sieving The situation gets worse as the shape of the particle changes
200um
100um
Volume of particle is now 2x106 um3
Diameter of sphere with same volume as particle
is now 156um

23. Equivalent Spheres
The best way of describing irregularly shaped particles is to compare some aspect of their shape or size to the diameter of a sphere.

24. Equivalent sphere.

25. Equivalent spheres

26. Characterising distributions
Whatever method we choose…...
We need to be aware that different techniques will give different results.
This is because we are measuring a different property of the particle;
e.g. a length or a Stokes’ diameter or a volume.

27. Tabulating Data 12.8% of the volume of the sample is contained within
particles having equivalent sphere diameters between
3.49 and 4.30 microns

28. Graphical data.

29. An MS2000 Measurement. 1. A source of light.
2. A means of passing the light through the particles to allow scattering.
3. A means of measuring the light intensity at a range of scattering angles.
4. A method of analysis which converts the measured scattering to a particle size distribution.

30. Modules.
The transmitter module containing the laser, power supplies and spatial filtering.
The sample area with any cell and sample dispersion accessories.
The receiver module containing the detector arrays
The computer.

31. Scattering from particles
Incident light
Small angle scattering
Large angle scattering
The way in which light interacts with particles is such that large particles cause light to be scattered strongly in the forward direction but very weakly at higher angles. Small particles scatter their light into larger angles but this light is very weak in comparison.
For this reason we find that when measuring large particles we get large amounts of data generated at relatively low obscuration since a lot of light is scattered from the particles. When measuring small particles the scattered light is weak by comparison and so a high obscuration is required in order to generate relatively small amounts of data.

32. Scattered Light
Large particles scatter light mainly in the forward direction i.e. at small angles.
Small particles scatter light at larger angles -but this scattered light is much weaker than forward scattered light.
We need to choose our light sources with care!

33. Laser Light Source
Intensity of laser source allows sensitive measurements of all sizes and low concentrations.
Monochromatic light helps resolution.
A Stable Laser output permits high reproducibility.
We need to be able to detect the scattering from the smallest particles in the sample. Since these do not scatter much light we need to irradiate them with an intense light source -a laser.
If we irradiated the particles with white light we would get many different distributions -one for each of the wavelenghts present. The would cause the distribution to be smeared out and we would lose the resolution.
The laser works best when it has warmed up -just like any piece of electronic equipment. The Ms2000 is designed to warm up quickly so after 15mins the instrument has reached a stable operating temperature.

34. Blue light Source Also uses a blue LED of 466nm wavelength
This allows the very small signals produced from sub micron particles to be detected.
Some of the red detectors are re-used for detecting the scattered blue light.
Using a smaller wavelength increase the scattering intensities produced by small particles. This makes small particle signals easier to detect.
The large angle and backscatter detectors are re-used to measure blue light. The need to be equipped with a dual weighting system so that they can respond correctly to both blue and red light.

35. The Red light optical System
Sample cell
Focal plane detector
Laser
Laser monitor
Obscuration monitor
Range Lens
The optical system differs from previous diffraction models since it does not use parallel light but diverging and converging beams.

36. Blue light set-up FP Laser
The blue light beam lies at an angle of 16 deg to the red beam, this allows both light sources to act independently whilst still being able to use the same detectors.

37. Improving sub-micron data
Backscatter signal fitting is now improved by modelling cell reflections which can contaminate backscatter signals.

38. Cell Reflection Model
Multiple reflections within the cell cause forward scattered light to contaminate the backscattered signals.
For very fine particles backscattered light can also contaminate the forward scattered light.
Modelling this behaviour allows for better prediction of backscatter signals and an improvement in sub micron accuracy.

39. Understanding Cell Reflection
g,w R
g,a I
Reflected, Scattered, Back
Scattered, Reflected, Back
Scattered, Reflected, Forward 1 2
Understanding Cell Reflection
It’s important that when measuring small particles the weak scattered light is nit contaminated by stronger reflected light that was originally forward scattered. The cell reflection model helps to predict what components of the light around the cell is reflected or scattered.

40. Sample region.
Particles must be well dispersed so that we are measuring, as far as possible, the scattering from individual particles.
Multiple scattering could be a problem for high obscurations.
Need to assess the effects of multiple scattering on size distribution - is it significant?
Multiple scattering occurs all the time, however, its effects are negligible. If we keep adding sample and thus increasing the obscuration then mutiple scattering will start to become significant and this will tend to cause an underestimation of particle size.

41. Effect of High Obscuration
High ring no
Detector
Wet cell
High ring no
scattering
indicates small
particles
Low ring no
Small particles scatter light at large angles so when light is caused to scatter to higher detectors then it is assumed that the light must have been scattered from small particles.
Increasing the obscuration (concentration) makes multiple scattering more likely. This leads to higher angle scattering which corresponds to smaller particle size.

42. Multiple Scattering
The effects of multiple scattering are negligible for a wide range of obscuration values but a very high levels of obscuration the effects increase dramatically.
But remember, you can have more confidence in your result if you know it has been calculated from good data. Signal to noise ratio is important.

43. The Whole Detector Array
There are 32 detectors on the focal plane detector
9 side scatter
2 large angle
2 back scatter
These are real detectors since the 2 large angle also detect blue scattered light and so do the 2 backscatter. This means that there are 8 detectors in all in this area.

44. How is the scattered light organised?
The laser is illuminating 100’s or 1000’s of particles at any instant.
The light scattered from these particles is focussed onto a detector.
The detector records the amount of energy falling onto its light sensitive zones.
The detector thus records the amounts of energy scattered at particular angles.

45. The Fourier transform Y Detector f X
Since particles of equal size scatter at equal angles, the scattered light from the particles will be parallel and thus brought to the same point on the focal plane; i.e. the detector.
By placing the detector in the focal plane of the lens particles of the same size in the beam will scatter their energy to the same point on the detector
The problem is that small particles might scatter at such a large angle that their light would miss the lens and so that information would be lost. This would set a limit on the size range of the lens.

46. The Reverse Fourier System
Lens
Detector
Wet cell
The reverse fourier lens is designed to capture small particle info by placing the sample nearer to the detector. In this way higher angle scattering is detected. If we consider three identical sized particles then each will produce the same scattering angle. The reason why the scattered light converges is that the angle of the light coming from the light changes according to its position on the lens. As this angle gets smaller the scattered beam but tilt upwards in order to keep the scattered angle constant. This does not work if the particle are allowed to spread over a large area d

47. Range lens A single range lens is used with a focal length of 160mm.
This allows for measurement of large particles whilst still maintaining alignment robustness.
This is limited by the spot size obtainable with large focal lengths. Since as the focal length increases so does spot size.

48. Analysis options General purpose Multimodal Monodispersed
With an explanation of which analysis model is best for your application

49. Detection system. Scattering pattern sampled at a range of angles.
Pattern must be captured in a very short time [ 10 ms ].
A large number of snaps must be collected.

50. Analysis. Transfer data to P.C.
Calculate size distribution as % in band.
Calculate undersize distribution.
Calculate derived parameters.

51. Theory of LALLS - aims .
The basic theory of LALLS [ Low Angle Laser Light Scattering ].
The method of analysis used in the Malvern Mastersizer range of instruments.
The important choices of parameters in performing an analysis.
When those choices are critical.
How to obtain information to allow you to make correct choices.

52. Scattering intensity vs. Angle.

53. Calculation of scattered light.
Mie model.
Optical parameters - refractive index and absorption.

54. Mie Theory
Dates from 1907/8
Accounts for the interaction of light with matter - solves Maxwell’s equations exactly
Valid for all sizes of particle, wavelengths, and scattering angles
Gives correct answers and accounts for secondary scattering

55. Mie Theory We need to feed Mie theory with more info….
Refractive of particle np
Refractive index of dispersant nd
Absorption of particle abs
The relative values if refractive index and absorption are calculate
np abs
nd nd
Although we need three parameters we arrange them into two - the relative values. This is because the scattering depend on what medium the particles are in rather than the particles themselves. Just think of ice cubes in water.

56. Fraunhofer scattering.
The scattering model generates a scattering surface which relates intensity ans detector number to particle size. This fraunhofer scattering pattern is very simple since the fraunhofer model does not take into account light transmitted through the particle or absorbed by it.

57. Mie scattering.
The Mie scattering surface is more complex since it does account for thelight coupled into the particle.
Note: the graph to the side of the scattering surface shows how the surface has been modified so that we can see all of the peaks. If this had not happened some of the peaks would be so small that we would not be able to see them.

58. Effects of optical parameters.20 %
100 90 80 70 60 10 50 40
Shows three graphs 2Mie theory and 1 fraunhofer. This shows that for large particles all distribution coincide and are therfore not dependent on optical properties. The red curve has the wron refractive index and shows some departure to the blue correct curve. The green curve has been generated by Fraunhofer and shows that because fraunhofer cannot interpret the extra energy on the scattering surface it fits it into the surface and then invents a population of particles to explain the extra energy. 30 20 10
0.1
1.0
10.0
100.0
Particle Diameter (µm.)

59. Fraunhofer approximation
Assumptions
Particle is opaque (applies to large particles, metals, pigments etc)
Based on slits and disc shaped particles
Size of particle is much greater than wavelength of the light illuminating it (D>>40l ISO um)
Scattering is low angle (<100) - forward scattering only
Scattering coefficient is 2.00 for all sizes of particle

60. Fraunhofer approximation Disadvantages of Fraunhofer
Incorrect answers!!
When are the answers incorrect?
Particles have some transparency (i.e. are small <25mm
Where the scattered angles become large and secondary scattering occurs (a ghost or unreal peak is then observed)
When the relative refractive index is small <1.3

61. Mie Theory
Give Mie theory a particle size distribution and it will happily calculate a scattering pattern.
The Mastersizer will produce a scattering pattern from a size distribution.
We need to turn the scattering pattern into a size distribution!
This is not easy!

62. Mie Theory 1. Question? 4 + 5 =? Ans = 9 2. What does 9 equal?
(81)0.5
(27/3)
8+1 3X
etc….etc….etc

63. Calculation of size distribution
Comparison
Scattering
Scattering
Mie
Size Distribution
Guess
Comparison
Scattering
Size distribution
A guesstimate distribution is created just so that we can employ Mie theory to calculate the scattering distribution. This is then compared to the original pattern and the distribution is modified if the two are not the same. The cycle continues until the calculated scattering pattern is identical to the measured pattern. When this occurs, the distribution that created the identical pattern is the one that reported to the user.

64. Calculation Routine Calculate approximate PSD.
Calculate corresponding scattered light.
Compare using residual.
Adjust PSD to improve match.
Compare using residual
Continue until match is minimised.

65. When to use Fraunhofer All particles >25um
Particles are completely opaque
Relative refractive index is high - usually in air only - not in fluids

66. Iteration process.
Model independent.
Constrained.

67. Model Independent. In Windows = Polydisperse.
Allow independent adjustment of all size channels in optimising fit.

68. Constrained models. Can only give the form constrained.
Mono-modal, bi-modal, multi-modal, Rosin-Rammler, Log-normal, Normal.

69. When to select constrained model.
1. Never.
2. When you have independent evidence to suppose that the model fits.
3. When you know no other distribution can occur.
4. Always after model independent.

70. Complementary information.
PCS.
Microscopy.

71. Microscopy

72. LALLS AND PCS

73. LALLS and PCS

74. Please remember…….
The quality of the result obtained depends mainly on the dispersion state and stability of the sample you wish to measure.
The biggest source of error in particle size analysis is the user.

75. Sources of variation 3 - 50% 2 - 30% 1 - 2% 0.5 - 2% Users Sampling
Sample
Handling
Units
1 - 2%
Optical Bench %

76. Characterising distributions
A particle size distribution contains a large amount of data.
To assist comparisons and examination we extract simpler quantities from the data known as averages or means.
However, there are lots of different ways of calculating a mean!

77. Mean.
The mean is an “average” particle size. There is no unique mean. We can average all particle diameters, weighting them according to their volumes, surface areas, numbers or any other physical characteristic.

78. Mean values Three spheres of diameters 1,2,3 units 1 2 3
What is the average size of these spheres?
Average size = (1+2+3) ÷ 3 =2.00
This is called the D[1,0] - the number, length mean

79. Different techniques give different means ...
None of the answer’s
are wrong they have just
been measured using
different techniques.

80. Using Means
We can describe our distribution to number, surface, volume or weight.
However, it is important to know how to interpret the difference between our descriptions.

81. Number and Volume Distributions
Size
(cm)
1-10
0.1-1
Total
Number of
Objects
7000
17500
%by
number
0.2
0.5
99.3
100.0
% by
Mass
99.96
0.03
0.01
100.0

82. Number, Surface and Volume
It is mathematically simple to interconvert between means but there are significant errors generated in doing so.
Errors in the measurement technique are compounded on conversion.

83. Significant Diameters
D(v, 0.1) -10% of the total volume of the distribution lies below this diameter.
D(v, 0.5) - the median diameter. 50% of the distribution lies either side of this point.
D(v, 0.9) -90% of the total volume of the distribution lies below this diameter.

84. Median.
The median of a particle size distribution is the size above [ and below ] which we can find 50% of the volume of all particles. It is commonly referred to as the 50th percentile, D50 or, more correctly, as D[v,0.5]. The latter emphasises the volume basis.

85. Volume Mean Diameter.
D[4,3] which is often referred to as the Volume Mean Diameter [ VMD ]

86. Significant diameters
D(3,2) - the equivalent surface area mean diameter - or the Sauter Mean Diameter.
D(4,3) - the equivalent volume mean diameter or the De Brouckere mean.

87. Derived diameters
D(v, 0.9)
D(v, 0.1)
Size um
D(3,2)
D(4,3)

88. How do you make sure you have a good result?
General appearance of result.
Quality of data
Inspect fit
Optical properties
Residual.

89. Choosing the refractive index.
From standard lists.
Measure in refractometer.
Estimate by analogy.
Average values for composite materials.

90. Choosing the absorption.
Standard lists.
Physical appearance ( microscope ).
Confirmation from concentration measurements.

91. Effect of choosing the wrong model
The effect of changing the presentation
Particle Diameter (µm.) % 10 20 30 40 50 60 70 80 90
100
0.01
0.1
1.0
10.0
100.0
1000.0

92. How do I tell if a presentation code is inappropriate.
Shape of curve
Examining the fit
Residual

93. Fit and residuals
To fit data, the software takes the data and the optical properties and performs a series of calculations.
The end result is the size distribution which is most likely given that data and optical properties.
The residual is a measure of the “goodness” of fit. The fit at any point can also be examined.

94. Fit and residuals A low residual (<1%) = A good result, right?
Not always!
Many very different shaped distributions can give similar low residuals.

95. Different distributions similar residuals
Differing plots, similar residuals
Particle Diameter (µm.) % 10 20 30 40 50 60 70 80 90
100
0.01
0.1
1.0
10.0
100.0
1000.0

96. More on fit and residuals
Examine how the fit “hugs” the data especially for the higher data channels.
This can flag inappropriate imaginary refractive indices if the particle refractive index is known.

97. Sample A - 0 imaginary

98. Sample A imaginary

99. Index matching Can use: Index matching oils
IPA (1.38) and Methyl Naphthalene (1.62) mixes

100. An index matching experiment on fumed silica

101. Other tips
If the material is a mix of known proportions take the average.
If structure is similar chemically to a compound of known refractive index, assume both are the same.

102. The imaginary refractive index
What is it?
It takes into account everything that happens on or in the particle other than scattering.
Absorption / reflection

103. What imaginary value do I use, and how do I get it?
Reference books?
No.
Examine the fit at different imaginary values
Microscopy

104. Examination under the microscope
Appearance
Imaginary RI
Example
Glass beads
0.001
Emulsions
0.01
Calcium Carbonate
0.1
Most materials
1.0
Pigments and metal powders

105. Volume Concentration Determination
Obscuration measured by machine.
Mie theory predicts light extinction.
Beer - Lambert law

106. Volume concentration -

107. Checking optical properties.
Absorption
Vol. conc. %
Residual
0.1153
1.986
0.001
0.0597
1.623
0.01
0.0140
3.111
0.1
0.0020
5.500
Real Vol. Conc.
0.073%

108. What about any errors?
The volume concentration equation assumes sphericity.
For extremely non spherical materials, the volume concentration calculated for the machine will be different.