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A GUIDEBOOKTO PARTICLE SIZE
ANALYSIS
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TABLE OF CONTENTS
1 Why is particle size important?
Which size to measure
3 Understanding and interpreting particle size distribution calculations
Central values: mean, median, mode
Distribution widths
Technique dependence
Laser diraction
Dynamic light scattering
Image analysis
8 Particle size result interpretation: number vs. volume distributions
Transorming results
10 Setting particle size specifcations
Distribution basis
Distribution points
Including a mean value
X vs.Y axis
Testing reproducibility
Including the error
Setting specifcations or various analysis techniques
Particle Size Analysis Techniques
15 LA-950 laser diraction technique
The importance o optical model
Building a state o the art laser diraction analyzer
18 SZ-100 dynamic light scattering technique
Calculating particle size
Zeta Potential
Molecular weight
23 PSA300 and CAMSIZER image analysis techniques
Static image analysis
Dynamic image analysis
26 Dynamic range o the HORIBA particle characterization systems
27 Selecting a particle size analyzer
When to choose laser diraction
When to choose dynamic light scattering
When to choose image analysis
29 Reerences
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Particle size inuences many properties o particulate materials and is
a valuable indicator o quality and perormance. This is true or powders,
suspensions, emulsions, and aerosols. The size and shape o powders inuences
ow and compaction properties. Larger, more spherical particles will typically ow
more easily than smaller or high aspect ratio particles. Smaller particles dissolve
more quickly and lead to higher suspension viscosities than larger ones. Smaller
droplet sizes and higher surace charge (zeta potential) will typically improve
suspension and emulsion stability. Powder or droplets in the range o 2-5m
aerosolize better and will penetrate into lungs deeper than larger sizes. For these
and many other reasons it is important to measure and control the particle size
distribution o many products.
Measurements in the laboratory are oten made to support unit operations tak-
ing place in a process environment. The most obvious example is milling (or size
reduction by another technology) where the goal o the operation is to reduce
particle size to a desired specifcation. Many other size reduction operations and
technologies also require lab measurements to track changes in particle sizeincluding crushing, homogenization, emulsifcation, microuidization, and others.
Separation steps such as screening, fltering, cyclones, etc. may be monitored by
measuring particle size beore and ater the process. Particle size growth may be
monitored during operations such as granulation or crystallization. Determining the
particle size o powders requiring mixing is common since materials with similar
and narrower distributions are less prone to segregation.
There are also industry/application specifc reasons why controlling and
measuring particle size is important. In the paint and pigment industries particle
size inuences appearance properties including gloss and tinctorial strength.
Particle size o the cocoa powder used in chocolate aects color and avor.
The size and shape o the glass beads used in highway paint impacts reectivity.Cement particle size inuences hydration rate & strength. The size and shape
distribution o the metal particles impacts powder behavior during die flling,
compaction, and sintering, and thereore inuences the physical properties o
the parts created. In the pharmaceutical industry the size o active ingredients
inuences critical characteristics including content uniormity, dissolution and
absorption rates. Other industries where particle size plays an important role
include nanotechnology, proteins, cosmetics, polymers, soils, abrasives,
ertilizers, and many more.
Why is
particle size important?Particle size is critical within
a vast number o industries.
For example, it determines:
appearance and gloss o paint
avor o cocoa powder
reectivity o highway paint
hydration rate & strength o cement
properties o die flling powder
absorption rates o pharmaceuticals
appearances o cosmetics
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WHICH SIZE TO MEASURE?
A spherical particle can be described using a single numberthe diameter
because every dimension is identical. As seen in Figure 1, non-spherical
particles can be described using multiple length and width measures (horizontal
and vertical projections are shown here). These descriptions provide greater
accuracy, but also greater complexity. Thus, many techniques make the useul
and convenient assumption that every particle is a sphere. The reported value istypically an equivalent spherical diameter. This is essentially taking the physical
measured value (i.e. scattered light, settling rate) and determining the size o the
sphere that could produce the data. Although this approach is simplistic and not
perectly accurate, the shapes o particles generated by most industrial processes
are such that the spherical assumption does not cause serious problems.
Problems can arise, however, i the individual particles have a very large aspect
ratio, such as fbers or needles.
Shape actor causes disagreements when particles are measured with dierent
particle size analyzers. Each measurement technique detects size through the
use o its own physical principle. For example, a sieve will tend to emphasize the
second smallest dimension because o the way particles must orient themselvesto pass through the mesh opening. A sedimentometer measures the rate o
all o the particle through a viscous medium, with the other particles and/or the
container walls tending to slow their movement. Flaky or plate-like particles will
orient to maximize drag while sedimenting, shiting the reported particle size in
the smaller direction. A light scattering device will average the various dimensions
as the particles ow randomly through the light beam, producing a distribution o
sizes rom the smallest to the largest dimensions.
The only techniques that can describe particle size using multiple values are
microscopy or automated image analysis. An image analysis system could
describe the non-spherical particle seen in Figure 1 using the longest and shortest
diameters, perimeter, projected area, or again by equivalent spherical diameter.
When reporting a particle size distribution the most common ormat used even o
image analysis systems is equivalent spherical diameter on the x axis and percent
on the y axis. It is only or elongated or fbrous particles that the x axis is typically
displayed as length rather than equivalent spherical diameter.
DIAMETER
VERTICAL
PROJECTION
HORIZONTAL
PROJECTION
fgure 1| SHAPE FACTOR
Many techniques make the general
assumption that every particle is a
sphere and report the value o some
equivalent diameter. Microscopy or
automated image analysis are the
only techniques that can describe
particle size using multiple values
or particles with larger aspect ratios.
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Perorming a particle size analysis is the best way to answer the question:
What size are those particles? Once the analysis is complete the user has
a variety o approaches or reporting the result. Some people preer a single
number answerwhat is the average size? More experienced particle scientists
cringe when they hear this question, knowing that a single number cannot
describe the distribution o the sample. A better approach is to report both a
central point o the distribution along with one or more values to describe thewidth o distribution. Other approaches are also described in this document.
CENTRAL VALUES: MEAN, MEDIAN, MODE
For symmetric distributions such as the one shown in Figure 2 all central values
are equivalent: mean = median = mode. But what do these values represent?
MEAN
Mean is a calculated value similar to the concept o average. The various mean
calculations are defned in several standard documents (re.1,2). There are
multiple defnitions or mean because the mean value is associated with the
basis o the distribution calculation (number, surace, volume). See (re. 3) or anexplanation o number, surace, and volume distributions. Laser diraction results
are reported on a volume basis, so the volume mean can be used to defne the
central point although the median is more requently used than the mean when
using this technique. The equation or defning the volume mean is shown below.
The best way to think about this calculation is to think o a histogram table show-
ing the upper and lower limits o n size channels along with the percent within this
channel. The Di value or each channel is the geometric mean, the square root o
upper x lower diameters. For the numerator take the geometric Di to the ourth
power x the percent in that channel, summed over all channels. For the denomi-
nator take the geometric Di to the third power x the percent in that channel,
summed over all channels.
Understanding and interpretingparticle size distribution calculations.
fgure 2|SYMMETRIC DISTRIBUTIONWHERE MEAN=MEDIAN=MODE
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The volume mean diameter has several names including D4,3. In all HORIBA
diraction sotware this is simply called the mean whenever the result is
displayed as a volume distribution. Conversely, when the result in HORIBA
sotware is converted to a surace area distribution the mean value displayed is
the surace mean, or D 3,2. The equation or the surace mean is shown below.
The description or this calculation is the same as the D4,3 calculation, except
that Di values are raised to the exponent values o 3 and 2 instead o 4 and 3.
The generalized orm o the equations seen above or D4,3 and D3,2 is shown
below (ollowing the conventions rom re. 2, ASTM E 799, ).
Where:
D = the overbar in D designates an averaging process
(p-q)p>q = the algebraic power o Dpq
Di = the diameter o the ith particle
= the summation o Dip or Diq, representing all particles in the sample
Some o the more common representative diameters are:
D10 = arithmetic or number mean
D32 = volume/surace mean (also called the Sauter mean)
D43 = the mean diameter over volume (also called the DeBroukere mean)
The example results shown in ASTM E 799 are based on a distribution o liquid
droplets (particles) ranging rom 240 6532 m. For this distribution the ollowing
results were calculated:
D10 = 1460 m
D32 = 2280 m
D50 = 2540 m
D43 = 2670 m
These results are airly typical in that the D43 is larger than the D50
the volume-basis median value.
MEDIAN
Median values are defned as the value where hal o the population resides
above this point, and hal resides below this point. For particle size distributions
the median is called the D50 (or x50 when ollowing certain ISO guidelines).
The D50 is the size in microns that splits the distribution with hal above and hal
below this diameter. The Dv50 (or Dv0.5) is the median or a volume distribution,
Dn50 is used or number distributions, and Ds50 is used or surace distributions.
Since the primary result rom laser diraction is a volume distribution, the deault
D50 cited is the volume median and D50 typically reers to the Dv50 without
including the v. This value is one o the easier statistics to understand and also
one o the most meaningul or particle size distributions.
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MODE
The mode is the peak o the requency distribution, or it may be easier to visualize
it as the highest peak seen in the distribution. The mode represents the particle
size (or size range) most commonly ound in the distribution. Less care is taken
to denote whether the value is based on volume, surace or number, so either run
the risk o assuming volume basis or check to assure the distribution basis. The
mode is not as commonly used, but can be descriptive; in particular i thereis more than one peak to the distribution, then the modes are helpul to describe
the mid-point o the dierent peaks.
For non-symmetric distributions the mean, median and mode will be three
dierent values shown in Figure 3.
DISTRIBUTION WIDTHS
Most instruments are used to measure the particle size distribution, implying an
interest in the width or breadth o the distribution. Experienced scientists typi-
cally shun using a single number answer to the question What size are those
particles?, and preer to include a way to defne the width. The feld o statistics
provides several calculations to describe the width o distributions, and these
calculations are sometimes used in the feld o particle characterization. The most
common calculations are standard deviation and variance. The standard deviation
(St Dev.) is the preerred value in our feld o study. As shown in Figure 4, 68.27%
o the total population lies within +/- 1 St Dev, and 95.45% lies within +/- 2 St Dev.
Although occasionally cited, the use o standard deviation declined when
hardware and sotware advanced beyond assuming normal or Rosin-Rammler
distributions.
Once model independent algorithms were introduced many particle scientists
began using dierent calculations to describe distribution width. One o the
common values used or laser diraction results is the span, with the strict
defnition shown in the equation below (2):
In rare situations the span equation may be defned using other values such as
Dv0.8 and Dv0.2. Laser diraction instruments should allow users this exibility.
An additional approach to describing distribution width is to normalize the
standard deviation through division by the mean. This is the Coefcient o
Variation (COV) (although it may also be reerred to as the relative standarddeviation, or RSD). Although included in HORIBA laser diraction sotware this
value is seldom used as oten as it should given its stature. The COV calculation
is both used and encouraged as a calculation to express measurement result
reproducibility. ISO13320 (re. 4) encourages all users to measure any sample
at least 3 times, calculate the mean, st dev, and COV (st dev/mean), and the
standard sets pass/ail criteria based on the COV values.
fgure 4| A NORMAL DISTRIBUTION
The mean value is anked by 1 and 2
standard deviation points.
fgure 3| A NON-SYMMETRIC DISTRIBUTION
Mean, median and mode will be three
dierent values.
MODE
MEDIAN
MEAN
MEAN +2 STD-2 STD
+1 STD68.27%
95.45%
-1 STD
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Another common approach to defne the distribution width is to cite three values
on the x-axis, the D10, D50, and D90 as shown in Figure 5. The D50, the median,
has been defned above as the diameter where hal o the population lies below
this value. Similarly, 90 percent o the distribution lies below the D90, and 10
percent o the population lies below the D10.
TECHNIQUE DEPENDENCE
HORIBA Instruments, Inc. oers particle characterization tools based on several
principles including laser diraction, dynamic light scattering and image analysis.
Each o these techniques generates results in both similar and unique ways.
Most techniques can describe results using standard statistical calculations
such as the mean and standard deviation. But commonly accepted practices or
describing results have evolved or each technique.
LASER DIFFRACTION
All o the calculations described in this document are generated by the HORIBA
laser diraction sotware package. Results can be displayed on a volume, surace
area, or number basis. Statistical calculations such as standard deviation and
variance are available in either arithmetic or geometric orms. The most common
approach or expressing laser diraction results is to report the D10, D50, and D90
values based on a volume distribution. The span calculation is the most common
ormat to express distribution width. That said, there is nothing wrong with using
any o the available calculations, and indeed many customers include the D4,3
when reporting results.
A word o caution is given when considering converting a volume distribution
into either a surace area or number basis. Although the conversion is supplied
in the sotware, it is only provided or comparison to other techniques, such as
microscopy, which inherently measure particles on dierent bases. The conver-
sion is only valid or symmetric distributions and should not be used or any otherpurpose than comparison to another technique.
fgure 5| THREE X-AXIS VALUES
D10, D50 and D90
Dv0.5 MEDIAN
Dv0.9Dv0.1
90%
below
this size
10%
below
this size
50%
below
this size
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DYNAMIC LIGHT SCATTERING
Dynamic Light Scattering (DLS) is unique among the techniques described in
this document. The primary result rom DLS is typically the mean value rom the
intensity distribution (called the Z average) and the polydispersity index (PDI) to
describe the distribution width. It is possible to convert rom an intensity to a
volume or number distribution in order to compare to other techniques.
IMAGE ANALYSIS
The primary results rom image analysis are based on number distributions.
These are oten converted to a volume basis, and in this case this is an accepted
and valid conversion. Image analysis provides ar more data values and options
than any o the other techniques described in this document. Measuring each
particle allows the user unmatched exibility or calculating and reporting particle
size results.
Image analysis instruments may report distributions based on particle length as
opposed to spherical equivalency, and they may build volume distributions based
on shapes other than spheres.
Dynamic image analysis tools such as the CAMSIZER allow users to choose a
variety o length and width descriptors such as the maximum Feret diameter and
the minimum largest chord diameter as described in ISO 13322-2 (re. 5).
With the ability to measure particles in any number o ways comes the decision
to report those measurements in any number o ways. Users are again cautioned
against reporting a single valuethe number mean being the worst choice o
the possible options. Experienced particle scientists oten report D10, D50, and
D90, or include standard deviation or span calculations when using image
analysis tools.
CONCLUSIONS
All particle size analysis instruments provide the ability to measure and report the
particle size distribution o the sample. There are very ew applications where a
single value is appropriate and representative. The modern particle scientist oten
chooses to describe the entire size distribution as opposed to just a single point
on it. (One exception might be extremely narrow distributions such as latex size
standards where the width is negligible.) Almost all real world samples exist as
a distribution o particle sizes and it is recommended to report the width o the
distribution or any sample analyzed. The most appropriate option or expressing
width is dependent on the technique used. When in doubt, it is oten wise to reer
to industry accepted standards such as ISO or ASTM in order to conorm to
common practice.
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Interpreting results o a particle size measurement requires an under-
standing o which technique was used and the basis o the calculations.
Each technique generates a dierent result since each measures dierent
physical properties o the sample. Once the physical property is measured a
calculation o some type generates a representation o a particle size distribution.
Some techniques report only a central point and spread o the distribution,
others provide greater detail across the upper and lower particle size detected.
The particle size distribution can be calculated based on several models: most
oten as a number or volume/mass distribution.
NUMBER VS. VOLUME DISTRIBUTION
The easiest way to understand a number distribution is to consider measuring
particles using a microscope. The observer assigns a size value to each particle
inspected. This approach builds a number distributioneach particle has equal
weighting once the fnal distribution is calculated. As an example, consider the
nine particles shown in Figure 6. Three particles are 1m, three are 2m, and
three are 3m in size (diameter). Building a number distribution or these particleswill generate the result shown in Figure 7, where each particle size accounts or
one third o the total. I this same result were converted to a volume distribution,
the result would appear as shown in Figure 8 where 75% o the total volume
comes rom the 3m particles, and less than 3% comes rom the 1m particles.
When presented as a volume distribution it becomes more obvious that the
majority o the total particle mass or volume comes rom the 3m particles.
Nothing changes between the let and right graph except or the basis o the
distribution calculation.
Particle size result intepretation:number vs. volume distributions
fgure 7| NUMBER DISTRIBUTION
fgure 8| VOLUME DISTRIBUTION
fgure 6| PARTICLES 1, 2 AND 3m IN SIZE
Calculations show percent by volume
and number or each size range.
D = 1m
VOLUME = 0.52m
% BY VOLUME = 0.52/18.8 = 2.8%
D = 2m
VOLUME = 4.2m
% BY VOLUME = 4.2/18.8 = 22%
D = 3m
VOLUME = 14.1m% BY VOLUME = 14.1/18.8 = 75%
TOTAL VOLUME
0.52 + 4.2 + 14.1 = 18.8m
30
25
20
15
10
5
0
1m 2m 3m
70
60
50
40
30
20
10
0
1m 2m 3m
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Another way to visualize the dierence between number and volume distribu-
tions is supplied courtesy o the City o San Diego Environmental Laboratory.
In this case beans are used as the particle system. Figure 9 shows a population
where there are 13 beans in each o three size classes, equal on a number basis.
Figure 10 shows these beans placed in volumetric cylinders where it becomes
apparent that the larger beans represent a much larger total volume than the
smaller ones.
Figure 11 shows a population o beans where it may not be intuitively obvious,
but there is an equal volume o each size, despite the wide range o numbers
present. It becomes apparent in Figure 12 when the beans are placed in
volumetric cylinders that each volumes are equal.
TRANSFORMING RESULTS
Results rom number based systems, such as microscopes or image analyzers
construct their beginning result as a number distribution. Results rom laser
diraction construct their beginning result as a volume distribution. The sotware
or many o these systems includes the ability to transorm the results rom
number to volume or vice versa. It is perectly acceptable to transorm image
analysis results rom a number to volume basis. In act the pharmaceutical
industry has concluded that it preers results be reported on a volume basis
or most applications (re. 6). On the other hand, converting a volume result
rom laser diraction to a number basis can lead to undefned errors and is only
suggested when comparing to results generated by microscopy. Figure 13 below
shows an example where a laser diraction result is transormed rom volume to
both a number and a surace area based distribution. Notice the large change in
median rom 11.58m to 0.30m when converted rom volume to number.
12
10
8
6
4
2
0
0.34 0.58 1.15 2.27 4.47 8.82 17.38 34.25
PARTICLE SIZENUMBER DISTRIBUTION
MEAN = 0.38m
MEDIAN = 0.30m
SA = 13467 cm/cm
STANDARD DEV = 0.40
NUMBER
AREA VOLUME
VOLUME DISTRIBUTION
MEAN = 12.65m
MEDIAN = 11.58m
SA = 13467 cm/cm
STANDARD DEV = 8.29
fgure 9| 13 BEANS OF EACH SIZE
fgure 10|THE SAME 39 BEANS PLACEDIN VOLUMETRIC CYLINDERS
fgure 11|EQUAL VOLUME OF EACH OFTHE THREE TYPES OF BEANS
fgure 12|EQUAL VOLUMES INVOLUMETRIC CYLINDERS
fgure 13|VOLUME DISTRIBUTION CONVERTEDTO AREA AND NUMBER
Conversion errors can result when
deriving number or area values rom
a laser diraction volume result.
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Setting particle size specifcationsThe creation o a meaningul and product-appropriate particle size
specifcation requires knowledge o its eect on product perormance in
addition to an understanding o how results should be interpreted or
a given technique. This section provides guidelines or setting particle size
specifcations on particulate materialsprimarily when using the laser diraction
technique, but also with inormation about dynamic light scattering (DLS) and
image analysis.
DISTRIBUTION BASIS
Dierent particle sizing techniques report primary results based on number,
volume, weight, surace area, or intensity. As a general rule specifcations should
be based in the ormat o the primary result or a given technique. Laser diraction
generates results based on volume distributions and any specifcation should be
volume based. Likewise, an intensity basis should be used or DLS specifcations,
volume or acoustic spectroscopy, and number or image analysis. Conversion to
another basis such as numberalthough possible in the sotwareis inadvisable
because signifcant error is introduced. The exception to this guideline is convert-
ing a number based result rom a technique such as image analysis into a volumebasis (re. 7). The error involved is generally very low in this scenario.
DISTRIBUTION POINTS
While it is tempting to use a single number to represent a particle size distribu-
tion (PSD), and thus the product specifcation, this is typically not a good idea. In
nearly every case, a single data point cannot adequately describe a distribution o
data points. This can easily lead to misunderstandings and provides no inormation
about the width o the distribution. Less experienced users may believe that the
average particle size can adequately describe a size distribution, but this implies
expecting a response based on a calculated average (or mean). I orced to use a
single calculated number to represent the mid-point o a particle size distribution,
then the common practice is to report the median and not the mean. The medianis the most stable calculation generated by laser diraction and should be the
value used or a single point specifcation in most cases.
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Rather than use a single point in the distribution as a specifcation, it is suggested
to include other size parameters in order to describe the width o the distribution.
The span is a common calculation to quantiy distribution width: (D90 D10) /
D50. However, it is rare to see span as part o a particle size specifcation. The
more common practice is to include two points which describe the coarsest
and fnest parts o the distribution. These are typically the D90 and D10. Using
the same convention as the D50, the D90 describes the diameter where ninetypercent o the distribution has a smaller particle size and ten percent has a larger
particle size. The D10 diameter has ten percent smaller and ninety percent larger.
A three point specifcation eaturing the D10, D50, and D90 will be considered
complete and appropriate or most particulate materials.
How these points are expressed may vary. Some specifcations use a ormat
where the D10, D50, and D90 must not be more than (NMT) a stated size.
Example: D10 NMT 20mD50 NMT 80m
D90 NMT 200m
Although only one size is stated or each point there is an implied range oacceptable sizes (i.e. the D50 passes i between 20 and 80m).
Alternatively, a range o values can be explicitly stated.
Example: D10 10 20mD50 70 80m
D90 180 200m
This approach better defnes the acceptable size distribution, but may be
perceived as overly complicated or many materials.
It may also be tempting to include a requirement that 100% o the distribution is
smaller than a given size. This implies calculating the D100 which is not recom-mended. The D100 result (and to a lesser degree the D0) is the least robust
calculation rom any experiment. Any slight disturbance during the measurement
such as an air bubble or thermal uctuation can signifcantly inuence the D100
value. Additionally, the statistics involved with calculating this value (and other
extreme values such as the D99, D1, etc.) arent as robust because there may
not be very many o the largest and smallest particles. Given the possible
broad spread o D100 results it is not recommended or use in creating specifca-
tions involving a statement that 100% o the particles are below a stated size.
INCLUDING A MEAN VALUE
Ultimately, the sophistication o the specifcation should be driven by how particle
size inuences product perormance. Given that some people ask about the
average size, it is not surprising that some specifcations are based on a mean
diameter. This approach is complicated by the act that there are several mean
values that can be calculated and reported in the result (re. 8). The most common
mean value noted when using laser diraction is the volume mean, or D4,3. The
D4,3 is very sensitive to the presence o large particles in the distribution. It is a
good idea to use or include the D4,3 in the specifcation i product perormance
is sensitive to the presence o large particles. The other mean value occasion-
ally used is the D3,2, or surace mean. This value is only typically used when the
product is an aerosol or spray.
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X VS.Y AXIS
Other published specifcations are based on the percent below a given particle
size such as: 50% below 20m and 90% below 100m. This type o specifcation
is based on points along the y axis (which reports requency percent) as opposed
to the x axis (which reports diameter) as in the previous examples. Although this
approach has been used in many specifcations, it is important to realize the dier-
ence between using the x (size) and y (percent) axes. All measurements includean error which should always be considered when setting a specifcation.
For the example shown in Figure 14, the D50 is 100m with an error o +/- 5% on
the x (size) axis. This error includes all sources such as sampling and sample prep-
aration. The same error becomes +/- 20% when translated to the y (percent) axis.
Stating an error o +/- 5% is more attractive than +/- 20%, even when expressing
the same actual error range. The degree to which the y axis error is exaggerated
vs. the x axis depends upon the steepness o the distribution curve.
There are applications where the percent below a given particle size is an impor-
tant result. Recently there has been interest in the presence o nanoparticles
(at least one dimension smaller than 100nm) in products such as cosmetics. The
sotware which calculates the PSD should be capable o easily reporting the per-
cent under any chosen sizein this case the percent below 100nm (Figure 15).
In the LA-950 sotware this is displayed as Diameter on Cumulative %. In the
example below the value or percent less than 100nm is reported as 9.155%.
Several points are worth mentioning in regards to setting a specifcation on the
percent below 100nm as in this example specifcally and or sub-micron materials
generally. The particle size distribution is dependent upon many actors including
the sample preparation method. The laser diraction technique works best within
a certain particulate concentration range. This sometimes requires that samples
undergo dilution. In some cases this dilution may change the state o the particles
and aect the apparent size distribution. Additionally, ultrasonic energy can be
applied to improve the dispersion o agglomerates which can signifcantly change
the result.
TESTING REPRODUCIBILITY
There are currently two internationally accepted standards written on the use o
laser diraction: ISO 13320 (re. 9) and USP (re. 10). Both standards state
that samples should be measured at least three times and reproducibility must
meet specifed guidelines. Note that this means three independent measure-
ments (i.e. prepare the sample, measure the sample, empty the instrument, and
repeat). The coefcient o variation (COV, or (std dev/mean)*100) or the measure-
ment set must be less than 3% at the D50 and less than 5% at the D10 and D90to pass the ISO 13320 requirements. These guidelines change to less than 10%
at the D50 and less than 15% at the D10 and D90 when ollowing the USP
requirements. Finally, the guidelines all double when the D50 o the material is
less than 10m.
While ollowing the ISO or USP guidelines to test reproducibility is suggested, it is
typically part o an internal specifcation or procedure. The specifcations shown to
potential customers typically dont include the reproducibility values.
fgure 15|REPORTING PSD PERCENTAGESMALLER THAN THE GIVEN SIZE
In this example, percentage o the
PSD is reported at 100nm.
fgure 14|MEASUREMENT ERROR
Error appears exaggerated on the
Y axis because o the narrowness
o the PSD
12
undersize error of+/-20%
size error
of+/-5%
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
20 40 60 80 100
SIZE IN m
%UNDER
120 140
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INCLUDING THE ERROR
The reproducibility errors discussed above should be investigated and minimized
because they play an important role in the fnal setting o a specifcation. Once the
specifcation based on product perormance has been determined, then the fnal
specifcation must be narrowed by the error range (re. 11). In the example shown
in Figure 16 the specifcation or the D50 is 100 +/- 20% (or 80120m) based on
product perormance. I the total measurement error is +/- 10% (using USPguidelines or the D50 value), the specifcation must be tightened to ~90110m
(rounded or simplicity) in order to assure the product is never out o the peror-
mance specifcation. For example, i the D50 is measured to be 110m, we are
certain the D50 is actually less than 120m even with a maximum 10% error.
This is why it is important to create robust standard operating procedures or any
material we wish to set a published specifcation or. Any combination o high
measurement error (usually stemming rom non-optimized method development)
and tight specifcations will make meeting that specifcation more difcult.
Why make lie harder than it need be?
DYNAMIC LIGHT SCATTERING
The primary results rom dynamic light scattering (DLS) systems are typicallyreported as an intensity distribution. Key values included in DLS-based specifca-
tions are the intensity-weighted average (oten called the z average) and the
polydispersity index (PI), which quantifes distribution width. Mean values or one
or more peaks can be calculated and included in the results. The results can be
transormed into a volume-based or number-based distribution when comparing
to other techniques such as laser diraction or microscopy.
fgure 16 |BUILDING SIZE SPECIFICATION
TO INCLUDE ERROR SOURCES
I the total measurement error is
+/- 10%, then the specifcation must
be tightened in order to assure the
product stays within perormance
specifcation.
13
80 85 90 95 100 105 110 115 120
SIZE IN m
SPECIFICATION INCLUDING ERROR
PRODUCT PERFORMANCE SPECIFICATION
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IMAGE ANALYSIS
The primary result reported by image analysis is a number distribution since the
particles are inspected one at a time. Setting specifcations based on the number
distribution is acceptable, but this is the one example where conversion to
another basis (i.e. volume) is both acceptable and oten preerred. As long as a
sufcient number o particles are inspected to ully defne the distribution, then
the conversion rom number to volume does not introduce unknown errors intothe result. The pharmaceutical industry discussed the subject at a meeting
organized by the AAPS (re. 6) and concluded that results are preerably reported
as volume distributions.
Particle size distribution specifcations based on the image analysis technique
oten include the mean, D10, D50, and D90 values. Care should be taken to avoid
basing specifcations on the number-based mean since this value may not track
process changes such as milling or agglomeration (re. 12). Conversion rom
number to volume distribution can be perormed with high accuracy by speciying
the typical particle shape (spherical, cylindrical, ellipsoidal, tetragonal, etc.).
Particle shape parameters such as roundness, aspect ratio, and compactnessare used to describe particle morphology. Specifcations or shape parameters
are typically reported using just the number-based mean value, so this is
recommended or setting specifcations.
CONCLUSIONS
The task o setting a particle size specifcation or a material requires knowledge
o which technique will be used or the analysis and how size aects product
perormance. Sources o error must be investigated and incorporated into the fna
specifcation. Be aware that, in general, dierent particle sizing techniques will
produce dierent results or a variety o reasons including: the physical property
being measured, the algorithm used, the basis o the distribution (number,
volume, etc.) and the dynamic range o the instrument. Thereore, a specifcation
based on using laser diraction is not easily compared to expectations rom other
techniques such as particle counting or sieving. One exception to this rule is the
ability o dymanic image analysis to match sieve results.
Attempting to reproduce PSD results to investigate whether a material is indeed
within a stated specifcation requires detailed knowledge o how the measure-
ment was acquired including variables such as the reractive index, sampling
procedure, sample preparation, amount and power o ultrasound, etc. This
detailed inormation is almost never part o a published specifcation and would
require additional communications between the multiple parties involved.
14
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The LA-950 combines the most popular modern sizing technique with stateo the art refnements to measure wet and dry samples measuring 10 nano-
meters to 3 millimeters. The central idea in laser diraction is that a particle will
scatter light at an angle determined by that particles size. Larger particles will scatter
at small angles and smaller particles scatter at wide angles. A collection o particles
will produce a pattern o scattered light defned by intensity and angle that can be
transormed into a particle size distribution result.
INTRODUCTION
The knowledge that particles scatter light is not new. Rayleigh scattering o light rom
particles in the atmosphere is what gives the sky a blue color and makes sunsets
yellow, orange, and red. Light interacts with particles in any o our ways: diraction,
reection, absorption, and reraction. Figure 17 shows the idealized edge diraction
o an incident plane wave on a spherical particle. Scientists discovered more than a
century ago that light scattered dierently o o dierently sized objects. Only the
relatively recent past, however, has seen the science o particle size analysis embrace
light scattering as not only a viable technique, but the backbone o modern sizing.
Bench-top laser diraction instruments
became practical with the advent o high
intensity, reasonably priced lasers and
sufcient computing power to process
the scattered light data. Once these
barriers to market entry were eliminated
the advantages o laser diraction over
other techniques were apparent: speedo analysis, application exibility, small
particle accuracy, and ease o use. The
ability to measure nano, micro and
macro-sized powders, suspensions,
and emulsions, and to do it within one
minute, explains how laser diraction
displaced popular techniques such as
sieving, sedimentation, and manual
microscopy.
RANGE IN MICRONS
10nm - 3,000 (3mm)
OPTIMAL APPLICATIONS
POWDERS, SUSPENSIONS,
AND EMULSIONS
WEIGHT 56kG (123 lbs)
FOOTPRINT
WIDTH 705mm (28)
DEPTH 565mm (22)
HEIGHT 500mm (20)
LASER
DIFFRACTION
TECHNIQUELA-950
fgure 17|DIFFRACTION PATTERNOF A PLANE WAVE
SCATTERING FROM
A SPHEROID
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Such an instrument consists o at least one source o high intensity, monochro-
matic light, a sample handling system to control the interaction o particles and
incident light, and an array o high quality photodiodes to detect the scattered
light over a wide range o angles. This last piece is the primary unction o a laser
diraction instrument: to record angle and intensity o scattered light. This inorma-
tion is then input into an algorithm which, while complex, reduces to the ollowing
basic truth:
The algorithm, at its core, consists o an optical model with the mathematical
transormations necessary to get particle size data rom scattered light. However,
not all optical models were created equally.
THE IMPORTANCE OF OPTICAL MODEL
In the beginning there was the Fraunhoer Approximation and it was good. This
model, which was popular in older laser diraction instruments, makes certain
assumptions (hence the approximation) to simpliy the calculation. Particles are
assumed
to be spherical
to be opaque
to scatter equivalently at wide angles as narrow angles
to interact with light in a dierent manner than the medium
Practically, these restrictions render the Fraunhoer Approximation a very poor
choice or particle size analysis as measurement accuracy below roughly 20
microns is compromised.
The Mie scattering theory overcomes these limitations. Gustav Mie developed a
closed orm solution (not approximation) to Maxwells electromagnetic equations
or scattering rom spheres; this solution exceeds Fraunhoer to include sensitivity
to smaller sizes (wide angle scatter), a wide range o opacity (i.e. light absorption),
and the user need only provide the reractive index o particle and dispersing
medium. Accounting or light that reracts through the particle (a.k.a. secondary
scatter) allows or accurate measurement even in cases o signifcant transpar-
ency. The Mie theory likewise makes certain assumptions that the particle
is spherical
ensemble is homogeneous
reractive index o particle and surrounding medium is known
Figure 18 shows a graphical representation o Fraunhoer and Mie models using
scattering intensity, scattering angle, and particle size (re. 13). The two models
begin to diverge around 20 microns and these dierences become pronounced
below 10 microns. Put simply, the Fraunhoer Approximation contributes a magni-
tude o error or micronized particles that is typically unacceptable to the user.
A measurement o spherical glass beads is shown in Figure 19 and calculated
using the Mie (red) and Fraunhoer (blue) models. The Mie result meets the
material specifcation while the Fraunhoer result ails the specifcation and splits
the peak. The over-reporting o small particles (where Fraunhoer error is signif-
cant) is a typical comparison result.
fgure 18 |REPRESENTATIONS OF
FRAUNHOFER (TOP) AND MIE
SCATTERING MODELS
Angle, energy and size are used as
parameters in these examples.
fgure 19|MIE (RED) AND FRANHOFER(BLUE) RESULTS FOR
SPHERICAL GLASS BEADS
16
LARGE PARTICLES SCATTER INTENSELY AT NARROW ANGLES
SMALL PARTICLES SCATTER WEAKLY AT WIDE ANGLES
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BUILDING A STATE OF THE ART
LASER DIFFRACTION ANALYZER
The basics o what needs to be measured and how its transormed into particle
size data are understood (re. 14). What constitutes a basic particle size analyzer
has also been discussed, but theres a wide gul between bare minimum and
state o the art. The latter is always the industry leader in accuracy, repeatability,
usability, exibility, and reliability. The current state o the art in laser diraction isthe Partica LA-950 eaturing two high intensity light sources, a single, continuous
cast aluminum optical bench (Figure 20), a wide array o sample handling sys-
tems, and expert refnements expected rom the fth revision in the 900 series.
Using two light sources o dierent wavelengths is o critical importance because
the measurement accuracy o small particles is wavelength dependent. Figure
21 shows the 360 light scattering patterns rom 50nm and 70nm particles as
generated rom a 650 nm red laser. The patterns are practically identical across
all angles and the algorithm will not be able to accurately calculate the dierent
particle sizes. Figure 22 shows the same experiment using a 405nm blue LED.
Distinct dierences are now seen on wide angle detectors which allows or
accurate calculation o these materials. Integrating a second, shorter wavelength
light source is the primary means o improving nano-scale perormance beyond
the bare minimum laser diraction analyzer.
CONCLUSIONS
The HORIBA LA-950 particle size analyzer uses the laser diraction method to
measure size distributions. This technique uses frst principles to calculate sizeusing light scattered o the particle (edge diraction) and through the particle
(secondary scattering reraction). The LA-950 incorporates the ull Mie scattering
theory to cover the widest size range currently available. Wide measurement
ranges, ast analyses, exceptional precision, and reliability have made laser dirac-
tion the most popular modern sizing technique in both industry and academia.
fgure 20| SIMPLIFIED LAYOUT OF THE LA-950 OPTICAL BENCH
1. Red wavelength laser diode or particles > 500nm
2. Blue LED or particles < 500nm
3. Low angle detectors or large particles
4. Side and back angle
fgure 21| LIGHT SCATTERING PATTERNSFOR 50nm AND 70nm PARTICLES
USING 650nm LASER
fgure 22| LIGHT SCATTERING PATTERNSFOR THE SAME SAMPLES
USING 405nm LED
fgure 23|30, 40, 50 AND 70 NANOMETERMATERIALS MEASURED
INDEPENDENTLY ON THE LA-950
USING THE BLUE LED
17
60
50
40
30
20
10
0.100 1.0000.010
DIAMETER (m)
q (%)
30 70
40
50 LATEX
STANDARDS
(m)
1
2
3
4 4
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The SZ-100 nanoPartica Dynamic Light Scattering (DLS) systemmeasures particle size, zeta potential, and molecular weight rom 0.3 nm to
8 m at concentrations ranging rom 0.1 mg/mL o lysozyme to 40% w/v.
This section explains the underlying principles used by the SZ-100 DLS system.
PARTICLE SIZE
Particle size can be determined by measuring the random changes in the
intensity o light scattered rom a suspension or solution. Small particles in
suspension undergo random thermal motion known as Brownian motion.
This random motion is measured to calculate particle size using the process
described below. A top view o the optical setup or particle size measurements
in the SZ-100 is shown in Figure 24.
DYNAMIC LIGHT
SCATTERING
TECHNIQUE
PARTICLE SIZE
ETA POTENTIAL
MOLECULAR
WEIGHT
SZ-100
RANGE IN MICRONS
0.3nm - 8m
OPTIMAL APPLICATIONS
NANOSUSPENSIONS
AND EMULSIONS UNDER 8m,ZETA POTENTIAL AND
MOLECULAR WEIGHT
WEIGHT 25kG (55 lbs)
FOOTPRINT
WIDTH 528mm (21)
DEPTH 385mm (18)
HEIGHT 273mm (11)
fgure 24|DYNAMIC LIGHTSCATTERING LAYOUT
FOR THE SZ-100
Light rom the laser light source illuminates the
sample in the cell. The scattered light signal is
collected with one o two detectors, either at a
90 degree (right angle) or 173 degree (back angle)
scattering angle. The obtained optical signal shows
random changes due to the randomly changing
relative position o the particles. This is shown
schematically in Figure 25.
BACKANGLEDETECTOR
RIGHT ANGLEDETECTOR
SAMPLELASER
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The signal can be interpreted using an autocorrelation unction. Incoming data
is processed in real time with a digital signal processing device known as a
correlator and the autocorrelation unction, shown in Figure 26 as a unction o
delay time,, is extracted.
The autocorrelation unction rom dynamic light scattering in Figure 26 shows
a sample where all o the particles are the same size, the baseline subtracted
autocorrelation unction, C, is simply an exponential decay o the ollowing orm:
EQUATION 1 C = exp(-2 )
is readily derived rom experimental data by a curve ft. The diusion coefcient
is obtained rom the relation =Dtq2 where q is the scattering vector, given by
q=(4n/)sin(/2). The reractive index o the liquid is n. The wavelength o the
laser light is , and scattering angle,. Inserting Dt into the Stokes-Einsteinequation then solves or particle size D
his the fnal step.
EQUATION 2 Dh=
kBT
Where:
Dh
= the hydrodynamic diameter
Dt
= the translational diusion coefcient
kB
= Boltzmanns constant
T = temperature
= dynamic viscosity
fgure 25| LIGHT SCATTERINGFLUCTUATIONS DUE TO
BROWNIAN MOTION VS. TIME
The optical signal shows random
changes due to the randomly changing
relative position o the particles.
fgure 26| AUTOCORRELATION FUNCTIONFROM DYNAMIC LIGHT
SCATTERING
For a sample where all o the
particles are the same size.
19
0.0
1.0
TIME (microseconds)
INTEN
SITY
(arb.units)
3Dt
1.0
0 100 200 300 400 500
1.5
2.0
DELAY TIME (sec)
ACF
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As shown in the top view, above, o the optical setup or zeta potential measure-
ments in the SZ-100, the particles are illuminated with laser light and, thereore,
the particles scatter light. A second beam o light (the reerence beam) is mixed
with the scattered beam in order to sensitively extract the requency shit in the
scattered light. The measured magnitude o the requency shit is then used to
determine the particle velocity. Equation 1 is used to calculate the electrophoretic
mobility () using the measured requency shit.
fgure 28
|
OPTICAL DIAGRAM OF THE SZ-100CONFIGURATION FOR ZETA POTENTIAL
ZETA POTENTIAL
Zeta potential is a measure o the charge on a particle surace in a specifc liquid
medium. This value o surace charge is useul or understanding and predict-
ing interactions between particles in suspension. Manipulating zeta potential is
a method o enhancing suspension stability or ormulation work, or speeding
particle occulation in applications such as water treatment. Zeta potential is
measured on the SZ-100 using the technique o electrophoretic light scatteringwhere particle motion is detected in an applied electric feld.
The charge on the surace o a particle inuences the ionic environment in the
region close to the particle surace. This ionic environment is typically described
using a double layer model the Stern layer o ions frmly attached adjacent to
the particle surace, and the diuse layer urther away rom the particle surace,
but still attracted to the particle such that these ions will move with the particle.
The boundary between the electric double layer and the ions in equilibrium in
the solution is called the slipping plane, as shown in Figure 27. Zeta potential is
defned as the potential measured in mV at the slipping plane distance rom the
particle surace.
To measure zeta potential a small quantity o sample is injected into a cell con-
taining two electrodes that are used to create an induced electric feld. Once the
electric feld is applied the particles move toward either the anode or cathode
depending on whether the suraces are positively or negatively charged. The
direction o the motion indicates positive vs. negative charge. The speed o the
particle motion is used to calculate the magnitude o the charge.
fgure 27| ZETA POTENTIAL
The zeta potential is the charge in
mV measured at the slipping plane.
slippingpane
zetapotential
dispersion
negatively chargedparticle surface
mV
TRANSMITTED LIGHTMONITOR (PD)
ZETA POTENTIALMEASUREMENT
FORWARD DETECTOR(PMT)
LASER LIGHTSOURCE CELL
REFERENCEBEAMS
ELECTRODE PARTICLE
MODULATOR
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4nEsin()2
3
21
EQUATION 1 =0
Where :
= the electrophoretic mobility
= the measured requency shit
= the laser wavelengthn = the reractive index o the medium
contains the angular light scattering inormation
Ater the electrophoretic mobility is determined using equation 1, the zeta
potential () is calculated using equation 2.
EQUATION 2 =2
(r)
Where:
= the electrophoretic mobility
= the zeta potential
= the dielectric permittivity o the medium
o = the viscosity
=(r) = a unction describing the ratio o the particle radius to the double layer
Zeta potential is oten measured as a unction o pH (or other additive property)
in order to determine the conditions at which there is zero zeta potential, also
known as the isoelectric point (IEP).
MOLECULAR WEIGHT
The SZ-100 can also be used to measure the molecular weight o proteins,
starches, polymers, dendrimers and other large molecules. The data can be
obtained by two dierent methods: dynamic light scattering and static lightscattering. Both methods are discussed below.
Dynamic Light ScatteringThere is a well-known empirical correlation between the diusion coefcient
o a macromolecule and its molecular weight known as the Mark-Houwink-
Sakurada equation.
Dt= kM
Where:
Dt =diusion coefcient
k =empirical constantM =molecular weight
=an empirical constant
The values or kand are ound empirically or polymer/solvent pairs. That is,
they must be specifed or the polymer, solvent, and temperature. These values
can be ound in the literature.
The advantages o this technique are that polymer concentration need not be
known and that molecular weight can be determined rapidly. It does, however,
rely on empirical constants and the nature o the average molecular weight.
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Static Light ScatteringThe SZ-100 can also be used in a static light scattering mode to measure the
molecular weight o proteins, small particles, and polymers. These results are
generated using a Debye plot (Figure 29) created by measuring the scattered
light at a single angle (90) at multiple sample concentrations. The intercept o
the Debye plot is used to determine the molecular weight and the slope is used
to calculate the second virial coefcient.
Molecular weight rom static light scattering experiments uses the Rayleigh
equation given below:
lim Kc = 1 + 2A2c
Where:
K = the Debye constant
C = the sample concentration
R = the Rayleigh ratio
Mw = the weight average molecular weightA2 = the second virial coefcient
The Debye constant is given by K=42n2 (dn/dc)2/(4NA) where n is the rerac-
tive index o the liquid, (dn/dc) is the reractive index increment, is the wave-
length o light in vacuo, and NA
is Avogadros number. In most cases, all o these
values are independent o molecular weight.
The limit given in the equation above deserves special attention. The equation
only works at the limit o zero angle. One practice required or larger macromol-
ecules is to use a multi-angle scattering instrument and extrapolate the result to
zero angle. For smaller molecules (Rg
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The microscope has always been the reeree technique in particlecharacterization since it is accepted as the most direct measurement o
particle size and morphology. Automating manual microscopy has been
driven by the desire to replace a tedious, somewhat subjective measure-
ment with a sophisticated technique or quantiying size and shape o
a sufcient number o particles to assure statistical confdence with the
end result. Analysts perorming manual microscopy tend to describe particle
shape using language such as round, blocky, sharp, fbrous, etc. By assigning
quantitative values rather than qualitative to various shape descriptors, image
analysis systems provide numerical distributions o well defned shape
parameters
Two distinct development paths have emerged over time diering in how thesample is introduced to the measurement zone: dynamic image analysis where
particles ow past one or more cameras and static image analysis where particles
sit on a slide moved by an automated stage or inspection by camera and
microscope.
Many basic unctions operate the same with either approach
(Figure 29): particles are presented to the measurement zone,
images are captured with a digital (CCD) camera, the particles are
distinguished rom the background, various size and shape parameters
are measured or each particle, and a result report is generated.
Additional eatures built into modern image analysis sotware
include the ability to automatically separate two particles
touching each other, flling holes, smoothing or removing
small protuberances, separating overlapping acicular
objects, and keeping track o incomplete objects in a feld
in order to recombine them once all felds are analyzed.
IMAGE
ANALYSIS
TECHNIQUEPSA300 |CAMSIZER
PSA300 static image analysis
RANGE IN MICRONS
0.5nm - 1,000m
OPTIMAL APPLICATIONS
POWDERS AND SUSPENSIONS
WEIGHT 34kG (75 lbs) w/o compute
FOOTPRINT
WIDTH 686mm (27)
DEPTH 483mm (19)HEIGHT 446mm (17.5)
CAMSIZER dynamic image analys
RANGE IN MICRONS
30m - 30mm
OPTIMAL APPLICATIONS
POWDERS
WEIGHT 34kG (75 lbs) w/o compute
FOOTPRINT
WIDTH 390mm (15)
DEPTH 850mm (33.5)
HEIGHT 220mm (9)
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STATIC IMAGE ANALYSIS
The samples measured by static image analysis typically rest on a slide that is
moved by an automated stage. With the PSA300 static image analysis system
a microscope and digital camera collect images o the particles as the slide is
scanned. Samples prepared on slides can include powders, suspensions, or
creams. Aerosol delivery orms such as metered dose inhalers or dry powder
inhalers can be inspected using static image analysis by actuating the device ontoa slide or measurement. In addition, particles in suspension (such as parenterals)
can be collected on a flter or characterization.
The majority o static image analysis measurements are made on powders,
typically used or solid oral dosage orms. Most powders require a sample prepa-
ration step prior to analysis. Powder preparation devicesusing either positive
pressure to impact on a hard surace or pulling and releasing a vacuumbreak
apart agglomerates and create an even dispersion on the slide. Ater the sample
has been prepared and the automated stage has presented multiple felds to the
optics and camera or capture, a series o image processing steps occur in the
sotware. The frst step is to separate the particles rom the background by setting
a parameter with some threshold value. Setting this threshold can be done
manually or automatically based on phases in the grayscale image or through a
contrast threshold unction based on the particle/background contrast.
Ater the threshold operation is completed several unctions may be applied to the
image to improve the edge defnition. The basic unctions o erosion and dilation
improve edge defnition by perorming opposite tasks o removing or adding dark
pixels at the particle edge. Advanced unctions using combinations o erosion and
dilation steps such as delineation and convex hull improve the edge defnition o
particles, leading to accurate area and perimeter determinations that are critical
or shape actor calculations. Other sotware unctions perorm the task o
separating touching particles including the crossed fbers in order to quantiy fber
length distributions and aspect ratios.
fgure 30|BASIC IMAGE ANALYSIS FUNCTIONS
Both static and dynamic image analysis
involve these basic steps.
75
60
45
30
15
0
100
80
60
40
20
0
1 2 5 10 30 50 100
IMAGE
ACQUISITION
Captured with a digital
(CCD) camera
THRESHOLDING
Separates particles rom
the background
CALCULATIONS
Generation o results
24
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DYNAMIC IMAGE ANALYSIS
Dynamic image analysis utilizes many o the same steps as static image analysis
with a ew notable exceptions. Sample preparation is completely dierent since
the sample itsel is moving during the measurement. Sample preparation steps
could include an ionizer to mitigate static interactions between particles thus
improving owability or a sample director to specifcally orientate particles through
the measurement zone. Many o the same image processing steps used orstatic image analysis are also used in dynamic systems, but it is less common
that the operator actively selects the unctions being utilized. A basic diagram o
the CAMSIZER dynamic image analysis system is shown in Figure 31.
The sample is transported to the measurement zone via a vibratory eeder where
the particles drop between a backlight and two CCD cameras. The projected par-
ticle shadows are recorded at a rate o more than 60 images (rames) per second
and analyzed. In this way each particle in the bulk material ow is recorded and
evaluated, making it possible to measure a wide range o particles (30 microns
to 30 millimeters) with extreme accuracy without needing operator involvement
to switch lenses or cameras as can be the case with other technologies. A great
depth o sharpness, and thereore maximum precision across the entire measur-
ing range, is obtained with the two-camera system. The zoom camera provides
maximum resolution down to the fne range, while the basic camera also records
larger particles and guarantees a high statistical certainty in the results.
Because o the size range measured by dynamic image analysis, this is a popular
technique or applications historically using sieves. By choosing the appropriate
size parameters the results can closely match sieve results, while providing the
benefts o quick, easy analyses with the bonus inormation about particle shape.
In those cases where matching historic sieve data is required the CAMSIZER can
be easily confgured to think like a sieve to ensure the closest possible correla-
tion. This is made possible by collecting shape inormation or each particle and
calculating how that shape would pass through a square mesh o known size.
Such a unction could be used to satisy existing quality control specifcations
while simultaneously measuring the true, non-biased particle size and shape
distributions or the frst time ever.
fgure 31| DYNAMIC IMAGE ANALYSIS
Particles all in ront o the zoom
and basic cameras that capture
digital images.
BASIC CAMERA ZOOM CAMERA
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LA-950 LASER DIFFRACTION
LA-300 LASER DIFFRACTION
SZ-100 DYNAMIC LIGHT SCATTERING
PSA300 IMAGE ANALYSIS
CAMSIZER IMAGE ANALYSIS
CAMSIZER XT IMAGE ANALYSIS
1nm 1m 1mm
10nm
0.3nm
100nm
0.5m
30m
1m
3mm
8m
600m
1000m
30mm
3mm
DYNAMIC RANGE OF THE HORIBA
PARTICLE CHARACTERIZATION SYSTEMS
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The decision process may be dierent i the instrument is being purchased
or a specifc application as opposed to a general analytical technique or
many possible samples. For specifc application it makes sense to search the
industry literature to determine i a particular technique is avored over others.
I or example the application is liposomes and 90% o all literature ound in this
feld is DLS, then the decision is simple. On the other hand, i this is the frst
particle size analyzer bought by a company or general purpose use, then exibility
and a wide dynamic range should be important actors.
Sometimes the goal to buy a new instrument includes being able to correlate
to existing data. Accomplishing this goal can range rom easy to difcult. Just
upgrading rom an older to newer model diraction analyzer could cause a change
in results. The changes originate rom many sources including dierences in
dynamic range, advances in algorithms, and mechanic improvements to
samplers. Switching rom an existing technique such as sieving to newer
techniques like laser diraction or dynamic image analysis could also lead to
changes in results. Data rom sieves are typically smaller than data rom laser
diraction depending on the shape o the particles. The less spherical the particle,
the greater the dierence will likely be. The CAMSIZER dynamic image analyzer
has multiple approaches built into the sotware to acilitate data matching
with sieves. As a general rule, data can be manipulated to approach existing
results, but understanding this issue during the selection process can ease the
implementation o
a new technique.
Particle size distribution is sufcient inormation or the majority o particle
characterization applications. But some techniques are higher resolution than
others. Ensemble technologies such as laser diraction and dynamic light
scattering are powerul techniques than are resolution limited compared to
high resolution techniques which are based on particle counting (such as electrozone counting or image analysis). I the goal o the measurement is fnding
small populations o particles larger or smaller than the main distribution, then
an investigation o the sensitivity to second distributions should be part o the
selection process.
Beginning the selection o a particle
size analyzer should start with asking
basic questions including:
Why am I making the measurement?
Must the new instrumentmatch historic data?
Do I need only particle size distribution,or do I need additional inormationsuch as shape or surace charge?
Selecting a particle size analyzer.
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Particle shape inormation may be either desirable or critical depending on the
degree to which shape aects product perormance. Particle shape inuences
bulk properties o powders including ow and compaction behavior and the
viscosity o suspensions. For specifc application such as glass beads used in high
way paint, shape is a critical actor or reectivity. When particle shape inormation
is required, microscopy and image analysis are the only techniques that delivery
the desired data. Manual microscopy provides basic qualitative size and shapeinormation, but automated image analysis generates quantitative data that is
statistically signifcant. For this reason, both dynamic and static image analysis
are growing techniques replacing manual microscopy.
Surace charge or zeta potential o suspensions is important inormation or
ormulators or chemists working on dispersion stability. For these applications a
DLS system providing both particle size and zeta potential (along with other such
as pH or conductivity) may be the best option.
Consider the application o wanting to measure the particle size distribution o
50nm colloidal silica. Just considering the size range o the sample indicates that
possible techniques include laser diraction or DLS. One question worth askingwould be will I need other capabilities in the uture? I I might need zeta potential
in the uture, this removes laser diraction rom the list o possible techniques.
I I might have particles >1m in the uture, this would eliminate DLS. Be
orewarned that uture requirements can be difcult to ascertain and additional
capabilities always carry incremental cost.
WHEN TO CHOOSE LASER DIFFRACTION
Laser diraction is the most popular particle size technique or reasons including
speed, ease o use, and exibility. The most basic laser diraction system can
measure solid particles in suspensions and emulsions. With the addition o a dry
powder eeder the instrument can then also measure dry powders in air. This is a
low concentration technique, so dilution is oten required. The complex reractive
index o the sample and diluent must be known or optimum accuracy, but this
inormation is easier to obtain than is oten indicated (more oten by competitors
than inormed scientists). The HORIBA LA-950 has a wide dynamic range capable
o measuring down to 30nm and up to 3000m. This unique ability to measure
particles
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WHEN TO CHOOSE DYNAMIC LIGHT SCATTERING
Dynamic Light Scattering (DLS) can measure suspensions and emulsions
rom 1nm to 1m. Both the lower and upper limits are sample dependent.
The lower limit is inuenced by concentration and how strongly the particles
scatter light. A low concentration sample o weakly scattering particles near
1nm can be extremely difcult or at least difcult to reproduce. The upper size
limit is determined mainly by the density o the particles. DLS algorithms arebased on all particle movement coming rom Brownian motion. Motion due
to settling is not interpreted correctly by DLS systems. In addition, particles
settled on the bottom o the sample cuvette can not be inspected by the laser
light source. Particles with a high density will settle more quickly than low
density particles. The upper limit o DLS may be 8m or emulsion samples
where the two phases have similar density. The upper limit o uranium particles
may be as small as 300nm. The upper limit o particles with a density o 1.7
may be around 1m.
Using DLS does not require any knowledge o the sample RI (it would be
required to convert rom intensity to volume distribution), or concentration.
What is required is viscosity, especially or higher concentration samples.Although most modern DLS systems claim the ability to work at higher
concentrations, this is again sample dependent. Serious DLS work could
involve a dilution study to determine the nature o the particle-particle
interactions and presence o multiple scattering. Easy samples are simply
a matter o pipetting the sample into a cuvette and clicking one button. More
sophisticated DLS systems can also measure other sample characteristics
including zeta potential, molecular weight, and second virial coefcient.
Generating this additional inormation may require a greater skill set o
the operator.
WHEN TO CHOOSE IMAGE ANALYSIS
Many laboratories are now replacing manual microscopy with automated
image analysis. While microscopy provides qualitative accuracy and shape
inormation, it requires automated image analysis to inspect the number o
particles requited to obtain statistically valid quantitative results. Choosing
image analysis is oten driven by the desire to generate results that are
accurate, sensitive to second populations, contains shape inormation, and
includes images o the particles. Dynamic image analysis is used in both
research and QC laboratories or particles ranging rom 30m to 30mm. Static
image analysis is typically a research tool or measuring particles in the 0.5 to
1000m range. Deciding between dynamic or static image analysis is seldom
difcult, as the applications are typically better served by one technique or the
other, as proven through application development studies.
REFERENCES
1 (PAGE 3)
ISO 9276-2:2001 : Representation o results o
particle size analysis Part 2: Calculation o average
particle sizes/diameters and moments rom particle
size distributions
2 (PAGE 3, 4)
ASTM E 799-03 Standard Practice or DeterminingData Criteria and Processing or Liquid Drop Size
Analysis
3 (PAGE 3)
TN154, Particle Size Result Interpretation:
Number vs. Volume Distributions, available at
www.horiba.com/us/particle
4 (PAGE 5)
ISO 13320-1 Particle size analysis Laser diraction
methods
5 (PAGE 7)
ISO 13322-2 Particle size analysis Image analysis
methods Part 2: Dynamic image analysis methods
6 (PAGES 8-9, 14)
Burgess, J., Duy, E., Etzler, F., Hickey, A., Particle
Size Analysis: AAPS Workshop Report, Cosponsored
by the Food and Drug Administration and the United
States Pharmacopeia, AAPS Journal 2004; 6 (3)
Article 20 (http://www.aapsi.org)
7 (PAGE 10)
TN154, Particle Size Result Interpretation:
Number vs. Volume Distributions, available at
www.horiba.com/us/particle
8 (PAGE 11)
TN156, Particle Size Result Interpretation: Under-
standing Particle Size Distribution Calculations,
available at www.horiba.com/us/particle
9 (PAGE 12)
ISO 13320-1 Particle size analysis Laser diraction
methods
10 (PAGE 12)
USP Light Diraction Measurement o
Particle Size
11 (PAGE 13)
Wheeler, D., How to Establish Manuacturing Speci-
fcations, posted on spcspress.com at http://www.
spcpress.com/pd/Manuacturing_Specifcation.pd
12 (PAGE 14)
Neumann et. al. What does a mean size mean?
2003 AIChE presentation at Session 39 Characteriza-
tion o Engineered particles November 1621 San
Francisco, CA
13 (PAGE 16)
ISO 13320, Particle size analysis Laser diraction
methods Part 1: General principles
14 (PAGE 17)
Understanding Calculation Level and Iterative
Deconvolution. www.horiba.com/us/particle
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Copyright 2012, HORIBA Instruments, Inc.
For urther inormation on this document
or our products, please contact us.
HORIBA Instruments, Inc.
34 Bunsen Drive
Irvine, CA 92618 USA
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