Volume 5 Number 1 January 2002
 University of Leeds
The importance of particle sizing to the coatings industry
Part 1: Particle size measurement
Alan Rawle
Malvern Instruments Ltd, Enigma Business Park, Grovewood Road, Malvern, Worcestershire, WR14 1XZ
The size of pigment particles within coatings formulations can have a dramatic effect on various coating properties,
such as opacity, tinting strength, viscosity and dispersion stability. Due largely to improvements in instrumentation,
particle sizing is becoming a routine analysis technique in many laboratories. However, there are several
techniques of measurement and many approaches to data analysis which can affect the particle size information
obtained. This paper attempts to explain the basics of particle size measurement and the problems and
confusions which can arise.
Keywords: particle size analysis, particle size distributions
INTRODUCTION
Particle size controls a number of properties
important to the paint chemist: optical properties,
including opacity; tinting strength; viscosity; and
sedimentation. Improved quality procedures mean
that paint companies must now control the
performance of their paints at the manufacturing
stage. This is largely in response to large
consumers, especially in the automobile and
similar industries, who impose tight tolerances
and specifications on their suppliers, and paint
manufacturers have had to respond. Traditionally,
the paint industry has not been a manufacturer of
chemicals – it buys what it needs and formulates
and packages the material.
This article attempts to explain the importance of
particle size to the modern paint company and to
illustrate it with relevant examples.
THE PARTICLE SIZE CONUNDRUM
Imagine measuring the size of a matchbox using a
ruler. A correct response might be that the
matchbox is 20 x 10 x 5mm. Each of these three
numbers represents only one aspect of the size of
the matchbox; it is not possible to describe the
three-dimensional matchbox with one unique
number. The situation is more difficult for a
complex shape like a grain of sand or a pigment
particle in a can of paint. A QA manager will want
one number only to describe such particles, in
order to track whether the average size has
increased or decreased since the last production
run, for example. This is the basic problem of
particle size analysis – how to describe a threedimensional object using one number only. As a
further illustration, consider Figure 1, which
shows some grains of sand. The difficulty in
establishing their sizes is obvious.
Figure 1: Particles of various sizes. How could they
be measured and compared?
The equivalent sphere
There is only one shape that can be described by
one unique number and that is the sphere. A
“50 µm diameter sphere” is described exactly.
Even for a regular shape such as a cube, for
example, the 50 µm may refer to an edge or to a
diagonal. With a shape such as a matchbox, it is
necessary to look for other properties that can be
described by one number. For example, the weight
is a single unique number, as is the volume and
the surface area.
If the weight of the matchbox is known, it could be
converted into the weight of a sphere, allowing
calculation of one unique number for the diameter
of the sphere of the same weight as the matchbox.
This is the equivalent sphere theory. It ensures
that we do not have to describe our three
dimensional particles with three or more numbers,
Vol 5 No 1 Jan 2002
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which, although more accurate, is inconvenient for
management purposes.
Clearly, this can produce some interesting effects
depending on the shape of the object. This is
illustrated by the example of the equivalent sphere
of a cylinder (Figure 2). However, if the cylinder
changes shape or size then its volume and weight
will change, and the equivalent sphere model will
at least be able to detect that it has become larger
or smaller.
Figure 2: Equivalent sphere of a cylinder of height
100 µm and diameter 20 µm
particle is used, this is equivalent to stating that
the particle is a sphere of this maximum
dimension. Likewise, if the minimum diameter or
some other quantity is used, this will give a
different answer as to the size of the particle.
Hence it is important to be aware that each
particle size characterisation technique will
measure a different property of a particle
(maximum length, minimum length, volume,
surface area etc.) and therefore will give a
different answer from another technique that
measures an alternative dimension. Figure 3
shows some of the different answers that are
possible for a single grain of sand.
Figure 3: Different particle size measures for the
same grain of sand
The volume equivalent spherical diameter for a
cylinder of 100 µm height and 20 µm in diameter is
around 40 µm.
Table 1 indicates equivalent
spherical diameters of cylinders of various ratios.
The last line may be typical of a large clay particle
that is disc shaped. It would appear to be 20 µm in
diameter, but as it is only 0.2 µm in thickness,
normally this dimension would not be considered.
An instrument that measures the volume of the
particle would give an answer around 5 µm. Hence
the possibility for disputing answers from different
techniques!
Table 1: Equivalent spherical diameters of cylinders
of various aspect ratios
Size of cylinder
Height
Diameter
Aspect ratio
Equivalent Spherical
Diameter
22.9
20
20
1:1
40
20
2:1
28.8
100
20
5:1
39.1
400
20
20:1
62.1
10
20
0.5:1
18.2
4
20
0.2:1
13.4
2
20
0.1:1
10.6
Note also that all of these cylinders would appear
the same size to a sieve, of say 25 µm, where it
would be stated that "all material is smaller than
25 µm". With laser diffraction these ‘cylinders’
would be seen to be different because they possess
different volumes.
Different techniques
If a particle is viewed under a microscope, then a
two dimensional projection of it is seen, and there
are several diameters that can be measured for its
characterisation. If the maximum length of the
2
Each technique is not wrong. They are all right; it
is simply that a different property of the particle is
being measured. Thus particle size measurements
on a powder can only seriously be compared by
using the same technique. This also means that
there cannot be anything like a particle size
standard for particles like grains of sand.
Standards must be spherical for comparison
between techniques. However, it is possible to
have a particle size standard for a particular
technique. This should allow comparison between
those instruments that use that technique.
Calculating average sizes
It may be useful to consider a specific example to
illustrate calculations of different average sizes.
Imagine three spheres of diameters 1, 2 and 3
units. The average size of these three spheres may
be thought to be 2.00, found by summing all the
diameters (Σd = 1 + 2 + 3) and dividing by the
number of particles (n=3). This is a number mean
(more accurately a number – length mean),
because the number of the particles appears in the
equation. In mathematical terms, this is the
D[1,0] mean because the diameter terms in the
numerator are to the power of 1 (d1) and there are
no diameter terms (d0) in the denominator.
However, a catalyst engineer might want to
compare these spheres on the basis of surface area
because the higher the surface area, the higher the
activity of the catalyst. The surface area of a
sphere is 4πr2. Therefore, to make comparison on
Vol 5 No 1 Jan 2002
the basis of the surface area of the spheres, the
diameters are squared, divided by the number of
particles, and the square root taken to get back to
a mean diameter. This is again a number mean
(number-surface mean); in mathematical terms
this is the D[2,0] mean.
A chemical engineer may want to compare the
spheres on the basis of weight or volume. This
would require finding the cube of the diameters,
dividing by the number of particles and taking a
cube root to get back to a mean diameter. Again
this is a number mean (number-volume or
number-weight mean); in mathematical terms this
can be seen to be the D[3,0] mean.
The main problem with the simple means, D[1,0],
D[2,0], D[3,0], is that the number of particles is
inherent in the formulae. This gives rise to the
need to count large numbers of particles. Particle
counting is normally only carried out when the
numbers are very low (in the ppm or ppb regions)
in applications such as contamination, control and
cleanliness. A simple calculation shows that in 1 g
of silica (density 2.5 g.cm-3) there would be around
760 x 109 particles if they were all 1 µm in size.
Hence, the concept of Moment Means needs to be
introduced, and it is with this concept that
confusion can arise. The two more important
moment means are the Sauter Mean Diameter
(Surface Area Moment Mean or D[3,2]) and the De
Brouckere Mean Diameter (Volume or Mass
Moment Mean or D[4,3]).
These means are
analogous to moments of inertia and indicate the
central point of the frequency around which the
(surface area or volume/mass) distribution would
rotate. They are, in effect, centres of gravity of the
respective distributions. The advantage of this
method of calculation is obvious. The formulae do
not contain the numbers of particles and therefore
calculations of the means and distributions do not
require knowledge of the number of particles
involved. Laser diffraction initially calculates a
distribution based around volume terms; this is
why the D[4,3] mean is reported in a prominent
manner.
Different techniques give different means
If an electron microscope is used to measure
particles, it is likely that the diameters would be
measured with a graticule, added up and divided
by the number of particles to get a mean result.
The D[1,0] number-length mean is generated by
this technique. If some form of image analysis was
used then the area of each particle might be
measured and divided by the number of particles,
generating the D[2,0] mean.
A technique such as electrozone sensing would
measure the volume of each particle and divide by
the number of particles, generating a D[3,0] mean.
Laser diffraction can generate the D[4,3] or
equivalent volume mean. This is identical to the
weight equivalent mean if the density is constant.
Thus, each technique is liable to generate a
different mean diameter as well as measuring
different properties of the individual particles.
This can be the basis of considerable confusion.
Number and volume distributions
Table 2 is adapted from an article in the New
Scientist (13 October 1991). There is a large
number of man-made objects orbiting the earth in
space and scientists track them regularly. They
have also classified them in groups on the basis of
their size.
Table 2: Size classification of man-made objects
orbiting earth
Size / cm
Number of objects
% by Number
% by Mass
10 – 1000
7000
0.2
99.96
1 – 10
17500
0.5
0.03
0.1 – 1.0
3500000
99.3
0.01
Total
3524500
100.00
100.00
The third column in Table 2 shows that 99.3% of
all particles are below 1 cm in size, evaluating the
data on a number basis. However, the fourth
column shows that 99.96% of the objects are
between 10 and 1000 cm in size, evaluating the
data on a mass basis. Note that the number and
mass distribution are very different and that
different conclusions would be drawn depending on
the distribution used. In addition, If the means of
the above distributions are calculated, they are
very different from each other; the number mean
is about 1.6 cm and the mass mean about 500 cm.
It is important to note that neither distribution is
incorrect, the data are just being examined in
different ways.
In making a space suit, for
example, it is easy to protect the wearer from the
7000 large objects, thus taking care of 99.96% of
the mass of all particles. However, it is more
important with a space suit to protect against the
small particles, which are 99.3% by number.
Interconversion between number, length and
volume/mass means
Mathematically, it is quite feasible to convert
between number, length and volume or mass
means. However, the consequences of such a
conversion can be rather surprising.
Imagine that an electron microscope measurement
technique is subject to an error of ±3% on the
mean size. When the number mean size is
converted to a mass mean size then, as the mass
mean is a cubic function of the diameter, the errors
will be cubed. In other words, there is ±27%
variation on the final result.
Vol 5 No 1 Jan 2002
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However, if calculating the mass or volume
distribution, for example by laser diffraction, then
the situation is different. For a stable sample,
measured under re-circulating conditions in a
liquid
suspension,
the
volume
mean
reproducibility may be around ±0.5%. If this
volume mean is now converted to a number mean,
the error of the number mean is the cube root of
0.5% or less than 1.0%.
In practice, this means that if using an electron
microscope to find a volume or mass distribution,
the effect of ignoring or missing one 10µm particle
is the same as ignoring or missing one thousand
1µm particles. Thus, one must be aware of the
great dangers of interconversion.
The software associated with most modern particle
sizers will calculate other derived diameters but
again great care must be taken in interpreting
these derived diameters. Different means can be
converted from one to another using the following
equations (Hatch-Choate transformation) [1,2]:
ln x NL = ln x gN + 0.5 ln 2 σ g
ln x NS = ln x gN + 1.0 ln 2 σ g
ln x NV = ln x gN + 1.5 ln 2 σ g
ln x NM = ln x gN + 2.0 ln 2 σ g
where
x gN
is the geometric mean (median) of the
number distribution
σg
is the geometric standard deviation
x NL
is the length mean diameter of the number
distribution of the particles
x NS
is the surface area mean diameter of the
number distribution of the particles
x NV
is the volume mean diameter of the number
distribution of the particles
x NM is the moment mean diameter of the number
distribution of the particles
It is important to be aware of the mean diameter
that is actually measured by the equipment and
those diameters that are really calculated or
derived from that first measured diameter. In
general, one can place more faith in the measured
diameter than on the derived diameters. In fact, in
some instances it can be very dangerous to rely on
the derived property. For example, a laser
diffraction analysis table may give a specific
surface area in m2.cm-3 or m2.g-1. However, this
4
should not be taken too literally. If an accurate
measure of the specific surface area is required, it
would be much better to use a surface area specific
technique such as the B.E.T. approach or mercury
porosimetry.
Remembering that each different technique
measures a different property (or size) of a particle
and that the data may be used in a number of
different ways to get a different mean result
(D[4,3], D[3,2] etc.), the question of which measure
of particle size should be used arises.
Taking a simple example of two spheres of
diameters 1 unit and 10 units respectively, the
simple number mean diameter is:
D[1,0] =
1 + 10
= 5.5
2
Thus the average size of the particles in the
system is 5.5 units. However, in a production
process environment a more important measure
may be the mass of material rather than the linear
diameter. As the mass mean is a cubic function of
diameter, the sphere of diameter 1 unit has a mass
of 1 unit and the sphere of diameter 10 units has a
mass of 103 = 1000 units. The larger sphere makes
up 1000/1001 parts of the total mass of the system.
The smaller sphere can be ignored because it
accounts for less than 0.1% of the total mass of the
system.
Thus, the number mean does not accurately reflect
where the mass of the system lies. The D[4,3]
mean is much more useful to (for example)
chemical process engineers. In the two sphere
example above, the mass or volume moment mean
would be calculated as follows:
D[ 4,3] =
14 + 10 4
= 9.991
13 + 10 3
However, imagine the production of wafers of
silicon or gallium arsenide. Here, if one particle
lands on a wafer it will tend to produce a defect. In
this instance the number or loading of the
particles is very important because one particle
causes one defect. In essence, this is the difference
between particle counting and particle sizing.
With counting, each particle must be recorded and
counted; the size is less important and only a
limited number of size classes may be required.
With sizing the absolute number of particles is less
relevant than the sizes or the size distribution of
the particles and more size bands may be required.
For certain applications (for example, a metered
dose inhaler for asthma sufferers) both the
concentration of particles and the particle size
distribution are important.
Vol 5 No 1 Jan 2002
Mean, Median and Mode - basic statistics
It is important to define these three terms as they
are so often misused both in statistics and in
particle size analysis:
Mean
This is an arithmetic average of the data. There
are various means that can be calculated for
particles, as explained above.
Median
This is the value of the particle size that divides
the population exactly into two equal halves, that
is, there is 50% of the distribution above this value
and 50% below. With the volume median, D[v, 0.5],
then 50% of the distribution by volume is above
this figure and 50% below.
Mode
This is the most common value of the frequency
distribution, or the highest point of the frequency
curve.
If the distribution is a Normal or Gaussian
distribution, the mean, median and mode will lie
in exactly the same positions (Figure 4). However,
if the distribution is bimodal (as shown in Figure
5), then the mean diameter may be almost exactly
between the two distributions as shown. Note
there are actually no particles that are this mean
size! The median diameter will lie 1% into the
higher of the two distributions because this is the
point that divides the distribution exactly into two.
The mode will lie at the top of the higher curve
because this is the most common value of the
diameter (but only just!). This example illustrates
that there is no reason why the mean, median and
mode should be identical or even similar; it
depends on the symmetry of the distribution.
Figure 4: Normal or Gaussian Distribution
METHODS OF PARTICLE SIZE
MEASUREMENT
In the preceding sections, it has been shown that
each measurement technique produces a different
answer because it is measuring a different
dimension of a particle. Some of the relative
advantages and disadvantages of the main
different methods employed will now be
considered.
Sieves
Sieving is an extremely old technique. It has the
advantage that it is cheap and is readily usable for
large particles such as those that are found in
mining. Allen has discussed the difficulties of
reproducible sieving [3]; the major disadvantages
to many users are the following:
• It is not possible to measure sprays or
emulsions
• Measurement for dry powders under 400#
(38µm) is very difficult. Wet sieving is said to
solve this problem but results from this
technique give poor reproducibility and
measurements are difficult to carry out.
• Cohesive and agglomerated materials, such as
clays, are difficult to measure.
• Materials such as 0.3 µm TiO2 are simply
impossible to measure and resolve on a sieve.
The method is not inherently high resolution
• The longer the measurement, the smaller the
answer, as particles orientate themselves to fall
through the sieve. This
means
that
measurement times and operating methods
(such as tapping) need to be rigidly
standardised.
• A true weight distribution is not produced;
rather the method relies on measuring the
second smallest dimension of the particle. This
can give some strange results with rod-like
materials, paracetamol in the pharmaceutical
industry for example.
• Tolerance. It is instructive to examine a table of
ASTM or BS sieve sizes and see the permitted
tolerances on average and maximum variation.
Sedimentation
Figure 5: Bimodal distribution
This has been the traditional method of
measurement in the paint and ceramics industries
and gives seductively low answers! The applicable
range is 2 – 50 µm [3,4].
The principle of measurement is based on the
Stokes’ Law equation:
US =
(ρ S − ρ F )D 2 g
18η
Vol 5 No 1 Jan 2002
5
where
US
is the terminal velocity of a settling particle
ρS
is the density of the settling particle
ρF
is the density of the surrounding medium
D
g
is the diameter of the settling particle
is the acceleration due to gravity
η
is the viscosity of the surrounding medium
The equipment used can be as simple as the
Andreason pipette or more complicated, involving
the use of centrifuges or X-rays.
Table 3: Comparison between Brownian motion and
gravitational settling
Displacement in 1.0 second (µ
µm)
In air at 20 °C
In water at 20 °C
Diameter of Brownian Gravitational Brownian Gravitational
settling
movement
settling
particle (µ
µm) movement
0.10
29.4
1.73
2.36
0.005
0.25
14.2
6.3
1.49
0.0346
0.50
8.92
19.9
1.052
0.1384
1.0
5.91
69.6
0.745
0.554
2.5
3.58
400
0.334
13.84
10.0
1.75
1550
0.236
55.4
Examination of this equation indicates one or two
potential pitfalls. The density of the material is
needed; thus the method is no good for emulsions
where the material does not settle, or for very
dense materials that settle quickly. The end result
is a Stokes diameter (DST) which is not the same
as a weight diameter, D[4,3], and is simply a
comparison of the particle’s settling rate to a
sphere settling at the same rate. The viscosity
term in the denominator indicates that it is
important to control temperatures very accurately;
typically a 1 °C change in temperature will
produce a 2% change in viscosity.
The sedimentation technique gives an answer that
is smaller than reality and this is why some
manufacturers deceive themselves. The main
disadvantages of the technique for pigment users
are the following:
Using Stokes’ Law it is relatively easy to calculate
settling times. It can be shown that a 1 µm particle
of SiO2 (ρ = 2.5 g.cm-3) will take 3.5 hours to
settle 1 cm under gravity in water at 20 °C.
Measurements are therefore extremely slow and
repeat measurements are tedious; hence the move
to increase ‘g’ by using a centrifuge. The
disadvantages of such an approach have been
discussed [5]. More specific criticisms of the
sedimentation technique have also been made [3].
• The technique cannot be used for mixtures of
differing densities; many pigments are a
mixture of colouring matter and extender/filler.
Stokes’ Law is valid only for spheres, which
possess the unique feature of being the most
compact shape for the volume or surface area they
possess. More irregularly shaped ‘normal’ particles
will possess more surface area than the sphere and
will therefore fall more slowly because of the
increased drag compared with their equivalent
spherical diameters. For objects like kaolins,
which are disc-shaped, this effect is even more
accentuated and large deviations between
measured and real values are to be expected.
Table 4: Settling times
Furthermore, with small particles there are two
competing processes - gravitational settling and
Brownian motion. Stokes’ Law only applies to
gravitational settling. Table 3 shows a comparison
between the two competing processes. It can be
seen that very large errors (approx. 20%) will
result if sedimentation is used for particles under
2 µm in size. Errors in excess of 100% will result
for particles under 0.5 µm in size.
Figure 6 shows the expected differences between
sedimentation and laser diffraction results.
6
• Speed of measurement. Average times are 25 to
60 minutes for measurement making repeat
analyses difficult and increasing the chances
for reagglomeration (Table 4) [6].
• Accurate temperature control is needed to
prevent temperature gradients and viscosity
changes.
• Use of X-rays. Some systems use X-rays and, in
theory, personnel should be monitored.
• Limited range. Below 2 µm Brownian motion
predominates and the system is inaccurate.
Above 50 µm settling is turbulent and Stokes’
Law again is not applicable.
Order of size
Approx time to
settle 1 m
10
Gravel
0.9 secs
1
Coarse sand
9 secs
0.1
Fine silt
100 secs
1.5 hours
Particle
diameter (mm)
0.02
Silt
0.001
Colloids
2.5 years
0.000001
Pigment particles
200 years
Vol 5 No 1 Jan 2002
Figure 6: Particle size results for kaolin measured by
sedimentation and laser diffraction
• Porous particles give significant errors as the
"envelope" of the particle is measured.
• Dense materials or large materials are difficult
to force through the orifice as they sediment
before this stage.
In summary, this technique is excellent for blood
cells, but of more dubious value in the
measurement of many industrial materials.
Microscopic evaluation
Electrozone sensing (Coulter Counter)
This technique was developed in the mid-1950s for
sizing blood cells, which are a virtually monomodal
suspension in a dilute electrolyte. The principle of
operation is very simple. A glass vessel has a hole
or orifice in it. Dilute suspension is made to flow
through this orifice and a voltage is applied across
it. As particles flow through the orifice the
capacitance alters; this change is indicated by a
pulse or spike in the voltage trace.
With older instruments the peak height is
measured and related to a peak height of a
standard latex. The method is not an absolute one,
but is of a comparative nature. Correction can be
made for problems of particle orientation through
the beam by measuring the area under the peak
rather than the peak height. For blood cells, the
technique is unsurpassed and the method is
capable of giving both a number count and volume
distribution. For real, industrial materials such as
pigments, there are several fundamental
drawbacks:
• It is difficult to measure emulsions and
impossible to measure sprays. Dry powders
need to be suspended in a medium and so
cannot be measured directly.
• Measurement must be carried out in an
electrolyte. For organic based materials this is
difficult as it is not possible to measure in
xylene, butanol or other poorly conducting
solutions.
• The method requires calibration standards,
which are expensive and change their size in
distilled water and electrolyte [3].
• For materials of relatively wide particle size
distribution the method is slow, as orifices have
to be changed and there is a danger of blocking
the smaller orifices.
• The lower limit of the method is determined by
the smallest orifice available, and it is not easy
to measure below 2µm or so. Certainly it is not
possible to measure TiO2 at 0.2µm.
Microscopy provides an excellent basis for the
visual evaluation of particles. The shape of the
particles can often be seen, and it may also be
possible to judge whether good dispersion has been
achieved or whether agglomeration is present in
the system. The method is relatively cheap and, for
some microscope systems, it is possible to use
image analysis to obtain numerical values for
particle size. It is of value to note that 1 g of 10 µm
particles (density 2.5 g.cm-3) contains 760 x 106
particles, which clearly can never all be examined
individually by microscopy.
Microscopy is not suitable as a quality or
production control technique beyond a simple
judgement of the type indicated above. Relatively
few particles are examined and there is the real
danger
of
unrepresentative
sampling.
Furthermore, if a weight distribution is measured
the errors are magnified. Missing or ignoring one
10 µm particle has the same effect as ignoring one
thousand 1 µm particles.
Electron microscopy requires elaborate sample
preparation and is slow. Few particles are
examined (maybe 2000 in a day with a good
operator) and there is rapid operator fatigue.
Again there is the problem of which dimension
should be measured; hence there can be large
operator-to-operator variability on the same
sample. In combination with diffraction studies,
microscopy becomes a very valuable aid to the
characterisation of particles.
Laser diffraction
This is sometimes called Low Angle Laser Light
Scattering (LALLS) but the generic term “light
scattering” is to be preferred. This method has
become the preferred standard in many industries
for characterisation and quality control. The
applicable range, according to ISO13320, is
0.1 - 3000 µm [7]. Light scattering instrumentation
has been developed over the last twenty years or
so. The method relies on the fact that diffraction
angle is inversely proportional to particle size.
Instruments consist of a source laser, a suitable
detector and some means of passing the sample
through the laser beam. A laser provides a source
of coherent, intense light of a fixed wavelength.
Vol 5 No 1 Jan 2002
7
He-Ne gas lasers (λ=0.632 µm) are the most
common as they offer the best stability (especially
with respect to temperature) and a better signal to
noise ratio than that of the higher wavelength
laser diodes. It is to be expected that when smaller
laser diodes can reach 600 nm and below and
become more reliable, they will begin to replace
the bulkier gas lasers.
The detector is usually a slice of photosensitive
silicon with a number of discrete detectors. It can
be shown that there is an optimum number of
detectors (16 - 32). Increased numbers do not mean
increased resolution. For the photon correlation
spectroscopy technique (PCS), used in the range
approximately 1 nm – 1 µm, the intensity of light
scattered is so low that a photomultiplier tube
together with a signal correlator is needed to make
sense of the information.
In practice, it is possible to measure aerosol sprays
directly by spraying them through the beam. This
makes a traditionally difficult measurement
extremely simple. A dry powder can be blown
through the beam by means of pressure and
sucked into a vacuum cleaner to prevent dust
being sprayed into the environment. Particles in
suspension can be measured by re-circulating the
sample in front of the laser beam.
Older instruments and some more recent
instruments rely only on the Fraunhofer
approximation, which makes the following
assumptions:
• Particles are much larger than the wavelength
of light employed (ISO13320 defines this as
being greater than 40λ, or 25 µm when a He-Ne
laser is used [7]).
• All particles scatter with equal efficiencies. The
scattering coefficient is assumed to be 2.00 for
all sizes of particle. The experimental value for
titanium
dioxide
approaches
5.0
at
approximately 0.25 µm so that for small
material, this is certainly not true.
• Particles are completely opaque and no light is
transmitted through. Hence only the light
‘classically’ scattered around the particle is
considered in the treatment. Only forward
scattered light in a very narrow angle is
considered.
These assumptions are never correct for many
materials, and for small materials they can give
rise to errors approaching 30%, especially when
the relative refractive index of the material and
medium is close to unity. When the particle size
approaches the wavelength of light, the scattering
becomes a complex function, with maxima and
minima present. The latest instruments use the
full Mie theory, which completely solves the
8
equations for interaction of light with matter. This
allows completely accurate results over a large size
range (typically 0.02 – 2000 µm). The Mie theory
assumes the volume of the particle as opposed to
the Fraunhofer approximation, which is a
projected area prediction.
The "penalty" for this complete accuracy is that
the refractive indices for the material and medium
must be known and that the absorption part of the
refractive index must be known or estimated.
However, for the majority of users this will present
no problems as these values are either generally
known or can be measured.
The laser diffraction method gives the end-user
the following advantages:
• The method is an absolute one set in
fundamental scientific principles. Hence there
is no need to calibrate an instrument against a
standard. In fact there is no real way to
calibrate a laser diffraction instrument.
Equipment can be validated, to confirm that it
is performing to certain traceable standards.
• A wide dynamic range. The best laser
diffraction equipment allows the user to
measure in the range from say 0.1 to 2000 µm.
Smaller samples (1nm – 1µm) can be measured
with the photon correlation spectroscopy
technique as long as the material is in
suspension and does not sediment.
• Flexibility. For example it is possible to
measure the output from a spray nozzle in a
paint booth. This has been used by nozzle
designers to optimise the viscosity, ∆P and hole
size, and layout, in order to get correct droplet
size. This has found extensive application in the
agricultural and pharmaceutical industries [8 –
10]. There is now an International Standard
(ISO) for laser diffraction [7], which should be
consulted for further information.
• Dry powders can be measured directly,
although as ISO13320 recommends (Section
6.2.3.2), the state of dispersion needs to be
assessed first using a pressure-size titration to
determine the extent of milling. This should be
followed by a wet versus dry dispersion to
confirm identical states of dispersion.
• Liquid suspensions and emulsions can be
measured in a re-circulating cell and this gives
high reproducibility and also allows dispersing
agents (the optimum concentration of Calgon
for TiO2) and surfactants to be employed to
ascertain the primary particle size. If possible
the preferred method would be to measure in
liquid suspension (aqueous or organics) for the
reasons discussed above.
Vol 5 No 1 Jan 2002
• The entire sample is measured. Although
samples are small (4 – 10 g for dry powders,
1 – 2 g for suspensions typically) and a
representative sample must be obtained, the
entire sample passes through the laser beam
and diffraction is obtained from all the
particles.
Figure 7: Adhesion force relative to gravitational
force
• The method is non-destructive and nonintrusive. Hence samples can be recovered if
they are valuable.
• A volume distribution is generated directly,
which is equal to the weight distribution if the
density is constant. This is the preferred
distribution for chemical engineers.
• The method is rapid, producing an answer in
less than one minute. This means rapid
feedback to operating plants and repeat
analyses are made very easily.
• Highly repeatable technique. This means that
the results can be relied on and the plant
manager knows that his product has genuinely
changed and that the instrument is not
‘drifting’.
• High resolution. Up to 100 size classes or more
can be provided.
THE “SIZE” OF SMALL MATERIALS
It is important to understand that not all dry
materials are present as separate particles, but
may exist as agglomerated or aggregated material.
The strength of the bonding in aggregates and
agglomerates increases dramatically as the
particle size reduces until, at around 0.5 µm, the
individual dry particles are no longer separable by
conventional means. Figure 7 indicates that 2 nm
particles are attracted to themselves or to other
particles to the extent that around 107 times the
accelerative force of gravity would be needed to
shear separate the surfaces. Clearly, this degree
of acceleration would be sufficient to break the
particle up rather then “de-agglomerate” the
system. Such particulate systems are therefore
irreversibly fused together when they come into
contact.
It is possible to make very small materials but
only in suspension.
For example, metal sols
(colloids) can be made down to particle sizes of
2 – 3 nm (0.002 – 003 µm) by various techniques.
Once these materials have been separated from
suspension and dried, it is not possible to “redisperse” them back to their original form. The
bonding
between
particles
then
becomes
essentially chemical in nature.
An easy way to determine if a particle system is
really small is to suspend it in water, if it is not
already in suspension.
Simple Stokes’ law
considerations (Table 5) indicate that a stable,
genuinely sub-micron material (a 1 µm ferrite
particle of density 5.5 g.cm-3 settles 1 mm in
approximately 5 minutes) would stay in
suspension for a few tens of minutes and not settle
out on the bottom of the container. A material
settling immediately to the bottom of a beaker of
water, leaving a clear supernatant, is likely to be
of at least 10 µm minimum size.
Table 5: Stokes’ Law calculations for particles of
differing size and density in water
Particle
diameter
Particle
density
Settling rate
/ mm.sec-1
Distance settled
in 1 minute / mm
1 µm
2.5
0.001
0.055
10 µm
2.5
0.09
5.51
100 µm
2.5
9.18
550.81
1 µm
5.5
0.0028
0.17
10 µm
5.5
0.2754
16.52
100 µm
5.5
27.54
1652.44
It should also be noted that the background level
of particulates in conventional unfiltered distilled
or de-ionised water is around 0.5 µm or so. Thus,
sample preparation and measurement would need
to be in filtered (0.02 µm or better) water in order
for small particles to be recognised. Small particles
would attach themselves to any larger background
material and thus re-aggregate. A genuine metal
sol of 2 – 5 nm, prepared in clean filtered solution,
can be measured using photon correlation
spectroscopy techniques.
Vol 5 No 1 Jan 2002
9
Wind-borne dust is around 1 – 10 µm in size and,
therefore, if a dry powder that was really 2 – 5 nm
were to be made, it would be impossible to keep it
in its container due to convection currents!
The usual supporting “evidence” for the smallness
of the particles is often provided by one or two
transmission electron micrographs (Figure 8)
showing individual collections or aggregates of
particles, the individual size of which is claimed to
be the fundamental size of the particle system.
material is to re-mill the dry product usually
ultrasonically in a wet system. The resulting
separated suspension must then be decanted and
charge–stabilised with the appropriate and
optimum amount of stabiliser. For TiO2 there will
be an optimum amount of stabiliser such as
Calgon (sodium hexametaphosphate), which is
usually determined empirically (Figure 9).
Figure 9: TiO2 dispersions with varying amounts of
Calgon stabiliser [4]
Figure 8: TEM micrograph of BaTiO3
THE EFFECTS OF PARTICLE SIZE ON
PAINT PROPERTIES
It is important to understand two major points
here:
1. These individual particles (or domains in
ferrites) are linked together chemically and
cannot be separated by conventional means in
the same way that we cannot separate out the
individual atoms, which could also be
considered the fundamental building blocks of
the system.
2. The number of such particles is viewed rather
than the mass or volume and hence we are in
reality examining the fine “dust” in the
system. An example of barium titanate is used
as an illustration (Figure 8). The single
micrograph shown illustrates very well the
difficulty of deciding what is an agglomerate
(loosely bound material), aggregate (tightly
bound) and what is a (free) particle.
A good illustration of all of the above points is
provided by titanium dioxide, which is normally
the smallest material encountered by particle size
technologists. TiO2 is made to a specification of
typically 0.25 – 0.30 µm, since this maximises the
scattering coefficient of the system. Kendall [11]
shows that there are actually no particles of this
size in the dry system – rather a collection of
aggregates and agglomerates up to 100 µm is
found in the dry material. This is demonstrated by
placing the dry material in a wet sieve of 20 µm
and shaking. No material passes through this
sieve. However, on adding water to the top of the
sieve, the material will then pass through.
As stated in the introduction to this review, the
particle sizes of pigments have marked effects on
the primary properties of the paints in which they
are used.
Opacity
For white pigments, the particle size affects the
opacity or scattering behaviour of the paint. The
amount of light scattered increases as the particle
size decreases, until further reduction in particle
size
decreases
scattering
and
reduces
transparency. For coloured pigments, scattering
and absorption are involved. The optimum
pigment volume concentration (PVC) for TiO2 is
about 17% by volume. This has been attributed to
the fact that at a PVC of about 0.17, the next fine
particle has a higher chance of joining an existing
fine particle than it does of forming an
independent scattering centre [12]. A fall-off in
opacity is apparent up to around 50% PVC, but an
increase of about 50% is noted [13] (Figure 10).
This increase is attributed to there being
insufficient medium to surround the pigment and
consequently pockets of air become included,
which increase the scattering power of the
pigment. Obviously increasing the PVC to the 50%
level would be completely uneconomical.
There is no magic dispersant for such systems.
Indeed, the only way to recover genuinely small
10
Vol 5 No 1 Jan 2002
Figure 10: Effect of pigment volume concentration on
opacity
Figure 11: Effect of volume percentage of pigment
on viscosity
Colour hue
The hue effect is illustrated by iron oxide
pigments, in which the smaller yellow particle
sizes (0.09 – 0.12 µm) give yellow toned reds and
the larger sizes (0.17 – 0.7 µm) give increasingly
bluer toned reds. Generally the finer size pigments
(<0.4 µm) produce brighter, purer shades.
For organic pigments, the finer the particle size,
the higher the tinting strength. However, here
again an optimum value is reached, beyond which,
finer particles do not increase the tinting strength,
and may actually reduce it.
Figure 11 illustrates the consequences of adding
thixotropic agents (for example, Aerosil – nanosize
SiO2), to prevent settling by increasing the
viscosity of the system. Ultrafine BaSO4 has been
used to reduce sagging [15], which is the
development of an uneven coating as the result of
excessive flow of paint on a vertical surface. Figure
12 shows the effect on transparency, viscosity and
gloss of BaSO4 against particle size.
Gloss
Figure 12: Effect of particle size
transparency and gloss
Tinting strength
on
viscosity,
The larger the particle size, the less glossy a white
paint will be. In fact matt paints can be produced
by incorporating large particle size TiO2. For
carbon black, the gloss decreases with decreasing
particle size.
Durability
The durability of certain pigments, many organics
for instance, is affected by particle size [4]. Data
related to Arylamide Yellow are shown in Table 6.
Table 6: Effect of particle size on arylamide yellow
Large particle size
Smaller particle size
Tinting strength
Lower
Higher
Opacity
Higher
Lower
Light fastness
Better
Poorer
Viscosity
The consistency of slurries is affected by the size of
suspended particles. The behaviour of zinc oxide in
oil [14] is illustrated by Figure 11.
Vol 5 No 1 Jan 2002
11
CONCLUSIONS
This review has given a flavour of the critical role
that particle size measurement plays in the
formulation of paints and coatings, and the
difficulties involved in such measurements have
been described. The practical application of
particle size measurements will be discussed in
Part 2 of this series.
REFERENCES
1.
T Hatch & S P Choate, J. Franklin Inst., 207, 369
(1929)
2.
A Jillavenkatesa, S J Dapkunas and L-S Lum,
NIST Special Publication 960-1, Particle Size
Characterization (January 2001)
3.
T Allen, Particle Size Measurement, 4th edition,
Chapman and Hall (1992)
4.
R Lambourne (ed), Paint and Surface Coatings –
Theory and Practice, Ellis Horwood Ltd (1993)
5.
G J J Beckers and H J Veringa, Powder Technology,
60, 245 (1989)
12
6.
D S Loubser, Flocculant additives and their role in
backfilling, SA Mining, Coal, Gold and Base
Minerals, 15 (November1989)
7.
ISO13320 Particle Size Analysis – Laser Diffraction
Methods Part 1: General Principles, ISO Standards
Authority (1999)
8.
K Deller et al, Pharmaceutical Technology, 108
(October 1992)
9.
G Hind, Manufacturing Chemist, 28 (Aug 1990)
10. M Wedd, ILASS Europe 8th Annual Conference,
Amsterdam (1992)
11. K Kendall, Powder Technology, 58, 151 (1989)
12. B H Kaye and G G Clark, Part.Syst.Charact., 9, 157
(1992)
13. J G Balfour, JOCCA, 6, 225 (1990)
14. R N Weltmann and N Green, J.Appl. Phys., 14, 569
(1943)
15. E Machunsky and J Winkler, Polymers Paint Colour
Journal, 180, 360 (1990)
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