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Particle size analysis
-Chapter 3
Size and hence surface area of particles affect:
The rate of drug dissolution and release from dosage forms
Flow properties of granules and powders.
Proper mixing of granules and powders.
Physical stability for suspensions.
Grittiness for topical formulation (powder must be
impalpable).
Irritation of the eyes for ophthalmic suspensions (small
particle must be used).
Importance of PSA
When determining the size of large solid usually we need to
measure at least three dimensions.
When determining the size of a sphere, it is possible to describe
the size using one dimension (diameter).
If a particles of powder is perfectly spherical, than it is possible
to describe the particle size by measuring the diameter of the
particle.
Dimensions
However, particles are often irregular and not perfectly
spherical.
Such irregular particles are considered to approximate to a
sphere (equivalent sphere), which can then be characterized
by determining its diameter.
Because the measurement is based on an hypothetical sphere,
which represents only an approximation to the true size of the
particle, the dimension is called equivalent sphere diameter.
Dimensions
It is possible to generate more than one sphere which is
equivalent to a given irregular particle shape.
Equivalent sphere diameter
Different equivalent diameters constructed around the same
particle. (Aulton’s 3rd ed.)
Equivalent sphere diameter
The equivalent spherical diameter, relates the size of a particle to the
diameter of a sphere having the same surface area or volume or
sedimentation rate or other factors. Examples of types of equivalent
diameters:
Surface diameter (ds) is the diameter of a sphere having the same
surface area as the particle in question.
Volume diameter (dv) is the diameter of a sphere having the same
volume as the particle in question.
Stokes diameter (dst) is the diameter of a sphere undergoing
sedimentation in a specific medium at the same rate as the asymmetric
particle.
Equivalent sphere diameter
Two topics will be covered in this Chapter:
1. Particle size distribution.
2. Methods for particle size analysis.
Particle size distribution
A powder population (a bulk of powder) which consists of
spheres or equivalent spheres of the same diameter is said to
be monodispersed and its characteristics can be described
by a single equivalent sphere diameter.
However, in pharmaceutical systems this situation is almost
never encountered.
Most powders contain particles with a range of different
equivalent diameters, i.e. they are polydispersed.
In order to be able to define the size distribution of
polydisperse powder samples, the size distribution can be
broken down into different size ranges, which can be
presented in the form of a histogram (or curve).
The histogram presentation allows also to compare the
characteristics of two or more polydisperse powder samples.
Particle size distribution
When the number (or weights) of particles lying within a
certain size range is plotted against a size range (or mean
particle size), a frequency distribution curve is obtained.
Such plots give a visual representation of the distribution that
an average diameter cannot achieve.
0
10
20
30
40
50
60
0.75 1.25 1.75 2.25 2.75 3.25 3.75
Mean of Size Range (um)
# o
f P
art
icle
s i
n E
ach
Siz
e
Ran
ge
PSD - Frequency distribution
The figure shown in the previous slide is representative of a normal
distribution: the particles are symmetrically distributed about a central
value.
The peak frequency value (called mode) separated the normal curve in
two identical halves, because the size distribution is fully symmetrical
(normal).
For normal distribution, mean = median =mode
mean – ‘average’ size of a population
median – size where 50% of the population is
below/above
mode – size with highest frequency
PSD - Normal distribution
In many cases, rather than plotting the number of particles (or
weight), laying within a specific size range, the percent particles
(or weight) in each size range (% frequency) can be plotted.
Size Range
(μm)
Mean of
Size Range,
di (μm)
Number of
particles in each
size range, ni
% Frequency
(ni/N)*100%
0.50 – 1.00 0.75 2 1.7
1.00 – 1.50 1.25 10 8.5
1.50 – 2.00 1.75 22 18.6
2.00 – 2.50 2.25 54 45.8
2.50 – 3.00 2.75 17 14.4
3.00 – 3.50 3.25 8 6.8
3.50 – 4.00 3.75 5 4.2
N=Σ ni= 118 100
PSD - % Frequency
PSD – Number vs Weight distributions
Number distributions imply that the data were collected by a
counting technique (microscopy, Coulter counter).
We are frequently interested in obtaining data based on weight
(weight distribution) which can be achieved by using
sedimentation or sieving techniques.
We can still convert number data (i.e. obtained by microscopy)
to weight data given the assumption that the general shape
and density of the particles are independent of the size range
of the sample.
Not all particles’ populations are characterized by normal size
distributions and the frequency distributions of such populations
exhibit skewness.
In this case, mean median mode.
PSD- Skewed distribution
Skewed distribution can sometimes be normalized by
replotting the equivalent particle diameter using a
logarithmic scale.
This is often referred to as log-normal distribution.
0
10
20
30
40
50
60
70
0 5 10 15 20
Mean of Size Range, um
# o
f P
art
icle
s
0
10
20
30
40
50
60
70
1 10 100
Mean of Size Range, um
# o
f P
arti
cle
s
PSD- Skewed distribution
a) Normal distribution: the mode separates the curves into two symmetrical
halves.
b) Positively skewed: a frequency curve with an elongated tail towards the
higher size range.
c) Negatively skewed: a frequency curve with an elongated tail towards
the lower size range.
d) Bimodal: the frequency curve containing two peaks (two modes).
PSD- Skewed distribution
Then, % frequency can then be used to produce the
cumulative percent frequency.
Cumulative % oversize: The total percent of particles
with size higher than the lower
limit of each class interval
Cumulative % undersize:
The total % of particles with size
lower than the upper limit of
each class interval
PSD – Cumulative frequency distribution
PSD – Cumulative frequency distribution
The median particle diameter corresponds to
the point that separates the cumulative
frequency curve into two equal halves,
above and below which 50% of the particles
lie (point a)
Just as the median divides a symmetrical
cumulative size distribution curve into two
equal halves, so the lower and upper quartile
points at 25% (b) and 75% (c) divide the
upper and lower ranges of a symmetrical
curve into equal parts.
PSD - Cumulative frequency distribution
Not all particle populations are characterized by symmetrical
or normal size distributions and the frequency distributions of
such populations exhibit skewness.
The degree of skewness can be estimated by determining the
interquartile coefficient of skewness (IQCS):
PSD - IQCS
a is the median diameter and b and c
are lower and upper quartile points.
The IQCS can take any value between
−1 and +1. If the IQCS is zero then the
size distribution is practically symmetrical
between the quartile points
)()(
)()(
baac
baacIQCS
PSD - IQCS
Methods of PS analysis
1. Sieve analysis method.
2. Microscopy.
3. Sedimentation in a liquid or gas.
4. Electrical sensing zone method
5. Laser light scattering
1. Sieving method
The most widely used method for measuring PSD (simple,
cheap, rapid and with little variability).
This method uses a series of standard calibrated sieves.
Sieves are generally used for grading coarser particles.
ISO range (45 – 1000 microns)
Equivalent diameter measured is the Sieve diameter (dA):
the width of the minimum square opening which the
particle will pass.
Sample preparation
Sieve analysis is usually carried out using dry powders.
For powders in liquid suspension wet sieving can be used.
Also for powders which tends to agglomerates during dry
sieving, wet sieving can be used.
1. Sieving method
Equipment
Sieve analysis uses wire woven stainless steel meshes
with known aperture diameters which form a
physical barrier to particles.
Most sieve analysis use a stack or nest of sieves
which has the smallest mesh above a collector tray
followed by meshes that become progressively
coarser towards the top of the stack of sieves.
1. Sieving method
Principle of measurement
The sieves are mounted on a mechanical shaker.
Powder is loaded on to the coarsest sieve at the
top of the assembled stack and the nest is
subjected to mechanical vibration.
After suitable time the particles that passes
through one sieve and retained on the next finer
sieve are collected and weighed.
Frequently the powder is assigned the size of the
screen through which it passes, on which it is
retained or the mean of the two values.
1. Sieving method
Limitations
Sieving errors would result from a number of variables including sieve
loading, intensity and time of agitation. Care must be taken to ensure
that the correct techniques are employed.
For materials >150 μm, a sieve analysis and particle size distribution is
accurate and consistent. However, for material that is finer than <150
μm, dry sieving can be significantly less accurate.
Sieve analysis assumes that all particles will be round (spherical). Less
spherical particles (e.g. elongated or flat) will give less reliable results.
Unsuitable for material that adheres to the sieve or forms clumps.
1. Sieving method
Standards for powders based on sieving
In order to characterize the particle size of a given powder,
the USP uses these standards descriptive terms: very coarse,
coarse, moderately coarse, fine, and very fine.
These terms are related to the proportion of powder that is
capable of passing through the openings of standard sieves.
1. Sieving method
Standards for powders based on sieving Very coarse (No. 8): All particles pass through a
No. 8 sieve and not more than 20% pass through
a No. 60 sieve. Coarse (No. 20): All particles pass through a No.
20 sieve and not more than 40% pass through a
No. 60 sieve.
Moderately coarse (No. 40): All particles pass
through a No. 40 sieve and not more than 40%
pass through a No. 80 sieve.
Fine (No. 60): All particles pass through a No. 60 sieve and not more than 40% pass through a No.
100 sieve
Very fine (No. 80): All particles pass through a No.
80 sieve. There is no limit to greater fineness.
1. Sieving method
Microscopy
Equivalent diameter:
da, dp, dF, dM can be determined
Range of analysis:
Light microscope: 1-1000 microns
Scanning electron microscope (SEM): 0.05 - 1 microns
Transmission electron microscope (TEM): 0.001 – 0.05
microns
2. Microscopy
Equivalent diameter
dp: perimeter diameter is based on a
circle having the same perimeter as the
particle.
da: projected area diameter is based
on a circle of equivalent area to that of
the projected image of a particle;
2. Microscopy
Equivalent diameter:
dF: Feret’s diameter is the distance between two parallel
tangents to the projected particle perimeter.
dM: Martin’s diameter is the is the length of a line that divides a
randomly oriented particle into two equal areas.
dF, dM are diameters which are averaged over many different
orientations to produce a mean value for each particle diameter.
dM corresponds to the dotted lines
2. Microscopy
Light microscopy - procedure
A suspension, diluted or undiluted, is
mounted on a slide and placed on a
mechanical stage.
The microscope eyepiece is fitted with a
micrometer by which the size of the
particles can be estimated.
The field can be projected onto a screen
where the particles are measured more
easily.
2. Microscopy
1. The number of particles that must be
counted (300-500) to obtain a good
estimation of the distribution makes the
method slow and tedious.
2. The diameter is obtained from only two
dimensions of the particle: length and
breadth. No estimation of the depth
(thickness) of the particle is ordinarily
available. (E.g. for a flaky particle the size
measurement might be overestimated).
Disadvantages
2. Microscopy
Advantage
Microscopic examination of a sample should be undertaken
even when other methods of particle size analysis are
available, because the presence of agglomerates and
particles of one or more than one component can be
detected properly by microscopy but overlooked by other
methods.
2. Microscopy
Equivalent diameter: dst(Stokes diameter)
Stokes equation:
gt
hd
os
st)(
18
dst= (Stokes diameter)
h = height or sedimentation distance
η = viscosity of the medium
v = rate of settling
t = time
ρs = density of the particles
ρo = density of dispersion medium,
g = acceleration due to gravity
18
0
2 gd
t
hv sst
3. Sedimentation method
The Stoke’s equation holds exactly only for spheres falling freely
without hindrance and at a constant rate.
The law is applicable to irregularly shaped particles of various
sizes as long as one realizes that the diameter obtained is a
relative particle size equivalent to that of sphere falling at the
same velocity as that of the particles under consideration. (i.e.
equivalent Stokes diameter).
The particles must not be aggregated or clumped together in
the suspension since such clumps would fall more rapidly than
the individual particles, and erroneous results would be
obtained (deflocculating agent may be needed).
3. Sedimentation method
Range of analysis:
Gravitational sedimentation: 5-1000 microns
Centrifugal sedimentation: 0.5-50 microns
3. Sedimentation method
Pipette method (Andreasen pipette)
The Andreasen apparatus usually consists of a
550-mL vessel.
In contains a 10-mL pipette sealed into a
ground-glass stopper.
When the pipette is in place in the cylinder, its
lower tip is 20 cm below the surface of the
suspension.
3. Sedimentation method
Pipette method (Andreasen pipette)
Particle size distribution can be determined by examining the
powder as it sediments.
The powder is dispersed uniformly or introduced as a thin layer in
a fluid.
The powder should not be soluble in the fluid, but should be
easily dispersed (wetting agent might be added to the fluid).
3. Sedimentation method
Balance method
The increase in weight of sedimented particles falling onto a
balanced pan suspended in fluid is recorded with respect to
time.
3. Sedimentation method
Alternative techniques
One of the limitations of gravitational sedimentation it is that it is
not suitable for particles < 5 microns:
in this case the test becomes too slow and less accurate.
This can be minimized by increasing the driving force of
sedimentation by replacing the gravitational force with a larger
centrifugal force (centrifugal sedimentation).
3. Sedimentation method
The electrical sensing zone method of particle characterization is
also known as Coulter Counter.
Equivalent diameter: dV (Volume diameter)
dV Diameter of the sphere having the same volume as the
particle
Range of analysis:
0.1- 1000 microns
4. Electric sensing zone method
Powder samples are dispersed in an electrolyte solution to form
a very diluted suspension.
The particle suspension is drawn through an orifice where
electrodes are situated on either side and surrounded by
electrolyte solution.
As the particle travels through the orifice, it displaces its own
volume of electrolyte solution.
The change in electrical resistance between the electrodes is
proportional to the volume of the particle (volume of the
electrolyte solution displaced).
4. Electric sensing zone method
4. Electric sensing zone method
This is a very accurate method of measurement, yet very
expensive and sophisticated.
Moreover dispersions must be sufficiently diluted to avoid the
occurrence of coincidence. Coincidence is when more than
one particle is present in the orifice at any one time. This may
result in two or more particles counted as one and therefore
inaccurate measurement (i.e. the equivalent diameter is based
on the volume of two particles rather than one).
4. Electric sensing zone method
Low angle light scattering
Equivalent diameters:
da and dV
Principle of measurement:
Scattering of light upon incidence with particle suspended in
air or a liquid.
Detection range:
0.5 to 1000 microns
5. Laser light scattering
Low angle light scattering
For particles (i.e. >1 µm) that are much larger than the wavelength of light,
any interaction with particles causes light to be scattered in a forward
direction with only a small change in angle (Fraunhofer diffraction). The
angle of scatter is inversely proportional to the particle diameter.
Laser light is passed through a dilute suspension of the particles. The light is
scattered by the particles, and is detected by detector which measures
light intensity over a range of angles.
5. Laser light scattering
Dynamic light scattering
Based on the Brownian movement (random motion of small
particles caused by collisions with the smaller molecules of the
suspended fluids).
It analyses the constantly changing patterns of laser light,
scattered by particles in Brownian movement.
The rate of change of scattered light can be related to the
particle size.
Range of analysis: 0.001 – 1 microns.
5. Laser light scattering